Acts 2:38
38 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 verse is very commonly used to teach that someone must repent "of their sins" to be saved, and is also the most common prooftext for Baptismal Regeneration - the doctrine that water baptism is what gives the new birth.
Therefore, it's vital to have a clear understanding of what Peter is teaching here.
The fact that Peter commands people to "repent" is often seen, as with every single other verse that uses the word, as a requirement to "repent of sins" to some unknown degree, in order to avoid being sent to Hell.
However, the verse doesn't say "repent of your sins", it says "repent". The word "repent" does not mean "turn from your sins", it means "to turn", and context determines what is being turned from. This is why God "repents" more than any other character in the Bible.
In Acts 2:38 in particular, we can tell that the command to "repent" is a command "to turn" from unbelief to belief, as we can look in a passage in Acts chapter 10, where the same speaker (Peter) says:
Acts 10:43-44, 47
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
44 While Peter yet spake these words, the Holy Ghost fell on all them which heard the word.
47 Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?
Above, Peter is preaching the Gospel, and the fact that the Jews killed the Messiah (Acts 10:38-42), just as he was doing in Acts chapter 2 (Acts 2:22-36).
Then, he says "whosoever believeth in him shall receive remission of sins", without mentioning water baptism. Finally, in verse 47, we see that people have the Holy Ghost, decidedly before being water baptized. Therefore, we see both the remission of sins, and the indwelling of the Holy Spirit, without water baptism.
What does this mean for Acts 2:38? In regard to its command to "repent", it is an instruction for the Jews to accept Jesus as their Messiah, by believing in Him, just as Peter says in the next chapter, "repent ye therefore, and be converted, that your sins may be blotted out" (Acts 3:19). This would be when they receive the Holy Ghost, as such a thing is contingent on faith (John 7:38-39, Ephesians 1:13). The "repentance" is being converted from unbelief to belief. The "forgiveness", in all of these passages, may also refer to sparing the Jews from the temporal punishments that awaited them, rather than justification.
Baptism, in Acts 2:38, is mentioned alongside the command to "repent" because it's the first step in obedience after faith (Acts 8:36-38), and part of the public witness required to be spared from the temporal judgment that awaited the Jewish nation (which would come to pass in 70 AD).
Furthermore, it's possible that the Acts 2:38 mention of receiving the "Holy Ghost" is referring to the outpouring of the Holy Ghost that had accompanying it signs and wonders, rather than the indwelling of the Holy Ghost that happens to every believer. This is evidenced by the fact that later in the book of Acts, we see believers who had been water baptized, and yet are still said not to have "received" the Holy Ghost:
Acts 8:14-17
14 Now when the apostles which were at Jerusalem heard that Samaria had received the word of God, they sent unto them Peter and John:
15 Who, when they were come down, prayed for them, that they might receive the Holy Ghost:
16 (For as yet he was fallen upon none of them: only they were baptized in the name of the Lord Jesus.)
17 Then laid they their hands on them, and they received the Holy Ghost.
Here, "receiving" the Holy Ghost - the same thing said in Acts 2:38 - is described as the Holy Ghost "falling upon them", and happens with the laying on of hands by the Apostles, which is almost certainly referring the outpouring, not indwelling.
Later, we see something similar in Acts 19:1-6, where believers hadn't "received" the Holy Ghost (Acts 19:2), and in context, it happens after the laying on of hands by Paul (Acts 19:6), and refers to the outpouring which had accompanying it signs and miracles (Acts 19:6). The same happened to the Apostle Paul himself, where he was "filled with the Holy Ghost" by the laying on of hands, before being baptized, and after believing (Acts 9:17-18).
And finally, we can look at the fact that Acts 2:38 is a response to a general question:
Acts 2:37-38
37 Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
38 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.
Compare the above to another question and answer given in Acts chapter 16:
Acts 16:30-31
30 And brought them out, and said, Sirs, what must I do to be saved?
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
In Acts 2, the question was a vague "what shall we do"? The answer includes "being baptized", because of course that's something everyone "should do". However, in Acts 16, the question is more targeted - "what must I do to be saved"? Therefore, the answer is given unambiguously - "believe on the Lord Jesus Christ, and thou shalt be saved".
Then, the passage in Acts chapter 16 goes on to explain how the jailer took Paul and Silas back to his house, and they preached the Gospel to his family, afterwards, baptizing all of them (Acts 16:32-33).
This again demonstrates that since water baptism is the first step in obedience for any new Christian, that it is natural to mention it alongside faith in the general instruction given in Acts 2:38. However, the fact that it's only occasionally included as an aside, and almost always left out completely, in close-ended statements about Salvation, shows that it is not itself a requirement for Salvation.
This passage does not teach that repentance of sin is required for Salvation, because, as is covered in this article, that would nullify the entire New Testament, and purpose of Christ coming in the first place.
It also does not teach that water baptism is required for Salvation, because as this article discusses, such a thing is not taught anywhere in the New Testament.