Trinity is not a Biblical word, but it is a term used to describe something that can be seen in the Bible.  Some try to define the Trinity beyond their understanding and end up delving into things that are too high for them. The fact that we don't fully understand the Trinity doesn't negate its reality. This is unwise and a sign of spiritual immaturity.  There is much that can be known, but much that God didn't tell us, so we can apply the principle of Deuteronomy 29:29 to it. 

God is one

1 Corinthians 8:4 As concerning therefore the eating of those things that are offered in sacrifice to idols, we know that an idol is nothing in the world, and that there is none other God but one.  
Deuteronomy 6:4 Hear, O Israel: The LORD our God is one LORD:

Isaiah 45:5 I am the LORD, and there is none else, there is no God beside me: I girded thee, though thou hast not known me:

Isaiah 43:10 Ye are my witnesses, saith the LORD, and my servant whom I have chosen: that ye may know and believe me, and understand that I am he: before me there was no God formed, neither shall there be after me. 

Isaiah 46:9 Remember the former things long past, For I am God, and there is no other; I am God, and there is no one like Me.

Isaiah 44:6 Thus saith the LORD the King of Israel, and his redeemer the LORD of hosts; I am the first, and I am the last; and beside me there is no God.

1 Corinthians 8:4-6 Therefore concerning the eating of things sacrificed to idols, we know that there is no such thing as an idol in the world, and that there is no God but one. For even if there are so-called gods whether in heaven or on earth, as indeed there are many gods and many lords, yet for us there is but one God, the Father, from whom are all things, and we exist for Him; and one Lord, Jesus Christ, by whom are all things, and we exist through Him. 

James 2:19 You believe that God is one. You do well; the demons also believe, and shudder.

Ephesians 4:4-6  There is one body and one Spirit, just as also you were called in one hope of your calling; one Lord, one faith, one baptism, one God and Father of all who is over all and through all and in all.

Deuteronomy 6:4  Hear, O Israel! The LORD is our God, the LORD is one!

God as plural

The name Elohim, translated God, is the plural form of El. While this is what is called a plural of plenitude pointing to the power and majesty of God, it certainly allows for the New Testament revelation of the Triunity of God.  Gen. 1:26; 3:22; 11:7; Isa. 6:8

Genesis 1:26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.

Isaiah 6:8 Also I heard the voice of the Lord, saying, Whom shall I send, and who will go for us? Then said I, Here am I; send me. 

John 14:9  He who has seen Me has seen the Father.

John 12:45 He who beholds Me beholds the One who sent Me.

Psalm 110:1 The LORD said to my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.

Three persons

John 14:16-17 And I (Jesus) will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.

John 14:23 If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him, and make Our abode with him.

Acts 2:32-33 This Jesus being exalted at the right hand of God, and having received from the Father the promise of the Holy Spirit, he has poured out this which you see and hear

John 5:7 For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.

Ephesians 4:4-6 There is one body, and one Spirit, even as ye are called in one hope of your calling; One Lord, one faith, one baptism, One God and Father of all, who is above all, and through all, and in you all.

Hebrews 9:14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?

1 Corinthians 12:4-6 Now there are diversities of gifts, but the same Spirit. And there are differences of administrations, but the same Lord. And there are diversities of operations, but it is the same God which worketh all in all.

John 14:16-18 & 26 And I (Jesus) will pray the Father, and he shall give you another Comforter, that he may abide with you for ever; Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know him; for he dwelleth with you, and shall be in you.  I will not leave you comfortless: I will come to you.  But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said to you.  

Matthew 28:19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: 

Matthew 3:16-17 And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened to him, and he saw the Spirit of God descending like a dove, and lighting upon him: And lo a voice from heaven, saying, This is my beloved Son, in whom I am well pleased.

Holy, holy, holy

Isaiah 6:3 And one cried to another, and said, Holy, holy, holy, is the LORD of hosts: the whole earth is full of his glory.

The Father is God

Ephesians 1:17 That the God of our Lord Jesus Christ, the Father of glory, may give to you the spirit of wisdom and revelation in the knowledge of him:

Ephesians 4:6 One God and Father of all, who is above all, and through all, and in you all.

Philippians 1:2 Grace be to you, and peace, from God our Father, and from the Lord Jesus Christ.

Jesus is God

Matthew 1:23 Behold, a virgin shall be with child, and shall bring forth a son, and they shall call his name Emmanuel, which being interpreted is, God with us.

Hebrews 1:8 But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom. 

Titus 2:13 Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ; 

1Timothy 3:16 And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached to the Gentiles, believed on in the world, received up into glory.

John 20:28 And Thomas answered and said to him (Jesus), My LORD and my God. 

1 John 5:20 And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life.  

Isaiah 9:6 For to us a child is born, to us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.

2 Peter 1:1 Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ:

Colossians 2:9-10 For in him (Jesus) dwelleth all the fulness of the Godhead bodily.  And ye are complete in him, which is the head of all principality and power

The Word (identified as Jesus in v. 14) as God

John 1:1-2 In the beginning was the Word, and the Word was with God, and the Word was God.  The same was in the beginning with God.

John 1:1-38  (for context) In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men.  And the light shineth in darkness; and the darkness comprehended it not.  There was a man sent from God, whose name was John.  The same came for a witness, to bear witness of the Light, that all men through him might believe.  He was not that Light, but was sent to bear witness of that Light.  That was the true Light, which lighteth every man that cometh into the world.  He was in the world, and the world was made by him, and the world knew him not.  He came to his own, and his own received him not.  But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:  Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.  And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.  John bare witness of him, and cried, saying, This was he of whom I spake, He that cometh after me is preferred before me: for he was before me.  And of his fulness have all we received, and grace for grace.  For the law was given by Moses, but grace and truth came by Jesus Christ.  No man hath seen God at any time, the only begotten Son, which is in the bosom of the Father, he hath declared him.  And this is the record of John, when the Jews sent priests and Levites from Jerusalem to ask him, Who art thou?  And he confessed, and denied not; but confessed, I am not the Christ.  And they asked him, What then? Art thou Elias? And he saith, I am not. Art thou that prophet? And he answered, No.  Then said they to him, Who art thou? that we may give an answer to them that sent us. What sayest thou of thyself?  He said, I am the voice of one crying in the wilderness, Make straight the way of the Lord, as said the prophet Esaias.  And they which were sent were of the Pharisees.  And they asked him, and said to him, Why baptizest thou then, if thou be not that Christ, nor Elias, neither that prophet?  John answered them, saying, I baptize with water: but there standeth one among you, whom ye know not;  He it is, who coming after me is preferred before me, whose shoe's latchet I am not worthy to unloose.  These things were done in Bethabara beyond Jordan, where John was baptizing.  The next day John seeth Jesus coming to him, and saith, Behold the Lamb of God, which taketh away the sin of the world.  This is he of whom I said, After me cometh a man which is preferred before me: for he was before me.  And I knew him not: but that he should be made manifest to Israel, therefore am I come baptizing with water.  And John bare record, saying, I saw the Spirit descending from heaven like a dove, and it abode upon him.  And I knew him not: but he that sent me to baptize with water, the same said to me, Upon whom thou shalt see the Spirit descending, and remaining on him, the same is he which baptizeth with the Holy Ghost.  And I saw, and bare record that this is the Son of God.  Again the next day after John stood, and two of his disciples; And looking upon Jesus as he walked, he saith, Behold the Lamb of God!  And the two disciples heard him speak, and they followed Jesus.Then Jesus turned, and saw them following, and saith to them, What seek ye? They said to him, Rabbi, (which is to say, being interpreted, Master,) where dwellest thou? 

 The Holy Spirit is God

 Acts 5:3-4 But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land?   Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied to men, but to God.

1 Cor. 6:11 And such were some of you: but ye are washed, but ye are sanctified, but ye are justified in the name of the Lord Jesus, and by the Spirit of our God.  (literally: the Spirit, our God.?)

Father sends the Son

John 3:16  For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. 

Father and Son send the Holy Spirit

John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said to you.  
Acts 2:33 Therefore (Jesus) being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear.

 
   
The Unity Of the Persons of the Godhead

John 10:30 I (Jesus) and my Father are one. 

John 17:11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are. 

John 14:11 Believe me that I (Jesus) am in the Father, and the Father in me: or else believe me for the very works' sake. 

John 15:26 But when the Comforter is come, whom I will send to you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:

John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said to you.

Romans 8:26-28 Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered.  And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God.  And we know that all things work together for good to them that love God, to them who are the called according to his purpose.

1 Corinthians 2:11 For what man knoweth the things of a man, save the spirit of man which is in him? even so the things of God knoweth no man, but the Spirit of God.

Father eternal

Isaiah 9:6 For to us a child is born, to us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.

Deuteronomy 33:27 The eternal God is thy refuge, and underneath are the everlasting arms: and he shall thrust out the enemy from before thee; and shall say, Destroy them.

Psalm 93:2 Thy throne is established of old: thou art from everlasting.

Son Eternal

Hebrews 1:12 And as a vesture shalt thou fold them up, and they shall be changed: but thou art the same, and thy years shall not fail.

Micah 5:2 But thou, Bethlehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth to me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting.

Holy Spirit eternal

Hebrews 9:14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?

Jesus receives the same worship as the Father

Revelation 5:11-14 And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands;  Saying with a loud voice, Worthy is the Lamb that was slain to receive power, and riches, and wisdom, and strength, and honour, and glory, and blessing.  And every creature which is in heaven, and on the earth, and under the earth, and such as are in the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power, be to him that sitteth upon the throne, and to the Lamb for ever and ever.  And the four beasts said, Amen. And the four and twenty elders fell down and worshiped him that liveth for ever and ever.

Philippians 2:9-10 Wherefore God also hath highly exalted him, and given him a name which is above every name:  That at the name of Jesus every knee should bow, of things in heaven, and things in earth, and things under the earth;

Other related verses

Romans 9:5 Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen.

Philippians 2:5-7 Let this mind be in you, which was also in Christ Jesus:  Who, being in the form of God, thought it not robbery to be equal with God: But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men:  (literally, "thought it not robbery" is "thought that being equal with God was not something that ought to be grasped at")

Colossians 1:15 Who (Jesus) is the image of the invisible God, the firstborn of every creature:

Holy Spirit in the beginning

Genesis 1:2 And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.

Spirit is the source of life and holiness 

Romans 8:2  For the law of the Spirit of life in Christ Jesus hath made me free from the law of sin and death.  
2 Corinthians 3:6 Who also hath made us able ministers of the new testament; not of the letter, but of the spirit: for the letter killeth, but the spirit giveth life.

The Father has glorified the Son

Acts 3:13-14 The God of Abraham, and of Isaac, and of Jacob, the God of our fathers, hath glorified his Son Jesus; whom ye delivered up, and denied him in the presence of Pilate, when he was determined to let him go.  But ye denied the Holy One and the Just, and desired a murderer to be granted to you;

Ananias lied to the Holy Spirit and God

Acts 5:3-4 But Peter said, Ananias, why hath Satan filled thine heart to lie to the Holy Ghost, and to keep back part of the price of the land?  Whiles it remained, was it not thine own? and after it was sold, was it not in thine own power? why hast thou conceived this thing in thine heart? thou hast not lied to men, but to God.

The Christian's body is temple of God/Holy Spirit

1Corinthians 3:16 Know ye not that ye are the temple of God, and that the Spirit of God dwelleth in you?

Ephesians 2:21-22  In whom all the building fitly framed together groweth to an holy temple in the Lord:  In whom ye also are builded together for an habitation of God through the Spirit.

The Father sealed Jesus

John 6:27 Labour not for the meat which perisheth, but for that meat which endureth to everlasting life, which the Son of man shall give to you: for him hath God the Father sealed.

God spoke through Jesus

Heb 1:1-3 God, who at sundry times and in divers manners spake in time past to the fathers by the prophets,Hath in these last days spoken to us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds; Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;

Matt. 1:20 Joseph, son of David, do not be afraid to take Mary as your wife; for that which has been conceived in her is of the Holy Spirit.

Luke 1:35 And the angel answered and said to her [Mary], "The Holy Spirit will come upon you, and the power of the Most High will overshadow you; and for that reason the holy offspring shall be called the Son of God.

 Additional Reading