There is only one baptism for a disciple of Christ. That baptism is to be "baptized in Christ," into his death.

How does this work? By what authority do we do this? It is done by the authority that Jesus gave when he ascended up to heaven:

Matthew 28:18-20: "And Jesus came up and spoke to them, saying, All authority has been given to me in heaven and on earth. Go therefore and make disciples of all the nations, baptizing them in the name of the Father and the son and the holy spirit, teaching them to observe all that I commanded you; and lo, I am with you always, even to the end of the age."

Jesus' instruction was to baptize in the name of the Father, son and the holy spirit. This instruction is the "how" of the matter. We are told elsewhere that we are baptized into Christ and this comes by the authority of Jesus' instructions. 

The conclusion here is that the authority of the Father, the son and the holy spirit give us the unique opportunity to be baptized into Christ, into being a part of his body. The "what" of the matter is explained in Romans 6:

Romans 6:1-11 (NASB) "What shall we say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it? Or do you not know that all of us who have been baptized into Christ Jesus have been baptized into his death?"

We are baptized to be a part of Jesus, a member of his (figurative) body and part of his self-sacrifice.

"Therefore we have been buried with him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life."

How do we walk in newness of life? It is only by the power of the holy spirit, which God chooses to give to those whom He has called to follow Jesus.

"For if we have become united with him in the likeness of his death, certainly we shall also be in the likeness of His resurrection, knowing this, that our old self was crucified with him, in order that our body of sin might be done away with, so that we would no longer be slaves to sin; for he who has died is freed from sin. Now if we have died with Christ, we believe that we shall also live with him, knowing that Christ, having been raised from the dead, is never to die again; death no longer is master over him. For the death that he died, he died to sin once for all; but the life that he lives, He lives to God."

The "name" of Jesus is here further shown to us. It is he who died to cancel the power of death.

"Even so consider yourselves to be dead to sin, but alive to God in Christ Jesus." 

Alive – by the holy spirit, and alive to God the Father and to Jesus His son.

Acts 2:38 may seem to introduce a contradiction:  Acts 2:38: "Peter said to them, Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the holy spirit."

This does not contradict anything we have just said, as it was a instruction by the Apostle Peter at Pentecost. He is simply telling those who were compelled to follow Jesus to be baptized in Jesus' name in contrast to the baptism of John the Baptist, which would have been the only baptism they knew about.

Addtional Resource:
Christian Questions Podcast
Episode #1306: "Are Christians Really Baptized Into Christ?"
Comparing several biblical baptisms with baptism into Christ
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