Is God a trinity?

Yes, please consider these points.

​Godhead, the Biblical term often equated with the doctrine of the trinity, is in the Bible three times, interestingly enough:

• Forasmuch then as we are the offspring of God, we ought not to think that the Godhead is like unto gold, or silver, or stone, graven by art and man's device. (Acts 17:29)
• For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, [even] his eternal power and Godhead; so that they are without excuse: (Romans 1:20)
• For in him dwelleth all the fulness of the Godhead bodily. (Colossians 2:9)

You can see all three Persons of the Godhead are God.
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The Father is God:

• But to us [there is but] one God, the Father, of whom [are] all things, and we in him; and one Lord Jesus Christ, by whom [are] all things, and we by him. (1 Corinthians 8:6)
• One God and Father of all, who [is] above all, and through all, and in you all. (Ephesians 4:6)
• And call no [man] your father upon the earth: for one is your Father, which is in heaven. (Matthew 23:9) 

The Son of God is God​:

• ¶ 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. (John 1:1-4)
• And without controversy great is the mystery of godliness: God was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory. (1 Timothy 3:16)
• He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that he might destroy the works of the devil. (1 John 3:8)
• 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. (Hebrews 1:8) 

The Holy Ghost, often called the Holy Spirit, is God:

• 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. (Genesis 1:2)
• [Whereof] the Holy Ghost also is a witness to us: for after that he had said before, This [is] the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; And their sins and iniquities will I remember no more. Now where remission of these [is, there is] no more offering for sin. (Hebrews 10:15-18)
• ¶ But a certain man named Ananias, with Sapphira his wife, sold a possession, And kept back [part] of the price, his wife also being privy [to it], and brought a certain part, and laid [it] at the apostles' feet. 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 unto men, but unto God. (Acts 5:1-4)

Here are some examples of the different Persons of the Godhead speaking.

The Father talking to Jesus:

• ¶ A Psalm of David. The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool. (Psalm 110:1)

Jesus talking about the Holy Ghost:

• Howbeit when he, the Spirit of truth, is come, he will guide you into all truth: for he shall not speak of himself; but whatsoever he shall hear, [that] shall he speak: and he will shew you things to come. He shall glorify me: for he shall receive of mine, and shall shew [it] unto you. (John 16:13-14) 

The Holy Ghost speaking:

• ¶ Wherefore (as the Holy Ghost saith, To day if ye will hear his voice, Harden not your hearts, as in the provocation, in the day of temptation in the wilderness: When your fathers tempted me, proved me, and saw my works forty years. Wherefore I was grieved with that generation, and said, They do alway err in [their] heart; and they have not known my ways. So I sware in my wrath, They shall not enter into my rest.) (Hebrews 3:7-11)

The law requires two or three witnesses to accept something as true:

• Whoso killeth any person, the murderer shall be put to death by the mouth of witnesses: but one witness shall not testify against any person [to cause him] to die. (Numbers 35:30)
• At the mouth of two witnesses, or three witnesses, shall he that is worthy of death be put to death; [but] at the mouth of one witness he shall not be put to death. (Deuteronomy 17:6)
• One witness shall not rise up against a man for any iniquity, or for any sin, in any sin that he sinneth: at the mouth of two witnesses, or at the mouth of three witnesses, shall the matter be established. (Deuteronomy 19:15)

And therefore, the testimony of God is true according to the law, because there are at least two witnesses:

•  It is also written in your law, that the testimony of two men is true. I am one that bear witness of myself, and the Father that sent me beareth witness of me. (John 8:17-18) 
• Grace be with you, mercy, [and] peace, from God the Father, and from the Lord Jesus Christ, the Son of the Father, in truth and love. (2 John 3) 
• For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one. (1 John 5:7)
• If we receive the witness of men, the witness of God is greater: for this is the witness of God which he hath testified of his Son. ¶ He that believeth on the Son of God hath the witness in himself: he that believeth not God hath made him a liar; because he believeth not the record that God gave of his Son. And this is the record, that God hath given to us eternal life, and this life is in his Son. (1 John 5:9-11)

God is plural in some verses:

• ¶ 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. (Genesis 1:26)
• ¶ And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: (Genesis 3:22)
• Go to, let us go down, and there confound their language, that they may not understand one another's speech. (Genesis 11:7) 
• ​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. (Isaiah 6:8) 
• ¶ Neither pray I for these alone, but for them also which shall believe on me through their word; That they all may be one; as thou, Father, [art] in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me. (John 17:20-21) 
  

All three Persons of the Godhead made man:

• The Spirit of God hath made me, and the breath of the Almighty hath given me life. (Job 33:4)
• But now, O LORD, thou [art] our father; we [are] the clay, and thou our potter; and we all [are] the work of thy hand. (Isaiah 64:8)
• Who is the image of the invisible God, the firstborn of every creature: For by him were all things created, that are in heaven, and that are in earth, visible and invisible, whether [they be] thrones, or dominions, or principalities, or powers: all things were created by him, and for him: And he is before all things, and by him all things consist. (Colossians 1:15-17)​

The Son is at the right hand of the Father:

• ¶ A Psalm of David. The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool. (Psalm 110:1) 
• For David himself said by the Holy Ghost, The LORD said to my Lord, Sit thou on my right hand, till I make thine enemies thy footstool. (Mark 12:36) 
• Hereafter shall the Son of man sit on the right hand of the power of God. (Luke 22:69) 
• ¶ If ye then be risen with Christ, seek those things which are above, where Christ sitteth on the right hand of God. (Colossians 3:1) 
• But he, being full of the Holy Ghost, looked up stedfastly into heaven, and saw the glory of God, and Jesus standing on the right hand of God, And said, Behold, I see the heavens opened, and the Son of man standing on the right hand of God. (Acts 7:55-56) 
• Looking unto Jesus the author and finisher of [our] faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God. (Hebrews 12:2) 
• Who is gone into heaven, and is on the right hand of God; angels and authorities and powers being made subject unto him. (1 Peter 3:22) 

And here's a picture of the trinity in just a few verses:

• And Jesus answering said unto him, Suffer [it to be so] now: for thus it becometh us to fulfil all righteousness. Then he suffered him. And Jesus, when he was baptized, went up straightway out of the water: and, lo, the heavens were opened unto 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. (Matthew 3:15-17) 
• And straightway coming up out of the water, he saw the heavens opened, and the Spirit like a dove descending upon him: And there came a voice from heaven, [saying], Thou art my beloved Son, in whom I am well pleased. (Mark 1:10-11)
• 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 28:19)