Baptism is the sign and seal of the new covenant: the believer, having trusted Christ, is immersed into His death and resurrection, publicly identifying with Him and being joined to His people. It is commanded by Jesus and received through faith, not a way of earning salvation.
Not a summary of these passages: the passages themselves. Read them, then come back to the study below.
The study
What the Scripture says
1
Jesus commanded it
Go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit. The early church obeyed immediately, baptizing three thousand on the day of Pentecost, and the Ethiopian asked for baptism the moment he believed.
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Then those who gladly received his word were baptized. There were added that day about three thousand souls.Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
As they went on the way, they came to some water, and the eunuch said, “Behold, here is water. What is keeping me from being baptized?”And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
He commanded the chariot to stand still, and they both went down into the water, both Philip and the eunuch, and he baptized him.And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
We who were baptized into Christ Jesus were baptized into his death, so that just as Christ was raised from the dead, we too might walk in newness of life. It is the visible picture of dying with Him and rising with Him.
Or don’t you know that all we who were baptized into Christ Jesus were baptized into his death? We were buried therefore with him through baptism to death, that just like Christ was raised from the dead through the glory of the Father, so we also might walk in newness of life. For if we have become united with him in the likeness of his death, we will also be part of his resurrection;Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
having been buried with him in baptism, in which you were also raised with him through faith in the working of God, who raised him from the dead.Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
It is the response of faith, not the work that saves
'Repent, and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of sins, and you will receive the gift of the Holy Spirit.' We are saved by grace through faith, not by works; baptism is the believer's obedient confession of that grace.
Peter said to them, “Repent, and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of sins, and you will receive the gift of the Holy Spirit.Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
for by grace you have been saved through faith, and that not of yourselves; it is the gift of God, not of works, that no one would boast.For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.
This is a symbol of baptism, which now saves you—not the putting away of the filth of the flesh, but the answer of a good conscience toward God, through the resurrection of Jesus Christ,The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ:
Those who received his word were baptized, and there were added that day about three thousand souls. By one Spirit we were all baptized into one body. Baptism is not a private event; it is the doorway into the visible church.
Then those who gladly received his word were baptized. There were added that day about three thousand souls.Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls.
For in one Spirit we were all baptized into one body, whether Jews or Greeks, whether bond or free; and were all given to drink into one Spirit.For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
praising God, and having favor with all the people. The Lord added to the assembly day by day those who were being saved.Praising God, and having favour with all the people. And the Lord added to the church daily such as should be saved.
Go,and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Or don’t you know that all we who were baptized into Christ Jesus were baptized into his death? We were buried therefore with him through baptism to death, that just like Christ was raised from the dead through the glory of the Father, so we also might walk in newness of life. For if we have become united with him in the likeness of his death, we will also be part of his resurrection;Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death? Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Peter said to them, “Repent, and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of sins, and you will receive the gift of the Holy Spirit.Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.
This is a symbol of baptism, which now saves you—not the putting away of the filth of the flesh, but the answer of a good conscience toward God, through the resurrection of Jesus Christ,The like figure whereunto even baptism doth also now save us (not the putting away of the filth of the flesh, but the answer of a good conscience toward God,) by the resurrection of Jesus Christ: