Since you were surprised at the statement in 1 Cor 15:29, you already realize that there is no teaching or context in the New Testament for interpreting that as one person being baptized in order to save another person who already died without being baptized. That occurred to you because it had been recently suggested, but the practice is not from the New Testament, is never taught or suggested there, and conflicts with what the Bible does say about life and death and judgment. That can't be Paul's meaning. In fact, there have been many interpretations of that verse, and it is difficult to be 100% sure what Paul was reminding the Corinthians of, except that he clearly thought they would understand the context.

I consider two ideas as being closely related to Paul's statement there in defense of believing in the resurrection. One is the teaching in Romans 6 that baptism is a direct identification with the death, burial, and resurrection of Christ. Baptism is bound together completely with believing in the resurrection of Jesus, and all who are baptized into him, "die" with him. That's part of the context. Along with the direct doctrinal connection between baptism and death and resurrection we have the context of martyrdom. In direct parallel in the passage Paul mentions daily danger (verse 30) in a rhetorical question with the same Greek word structure as the question about baptism for the dead. He seems to be reminding the reader, then and now, of the reality of martyrdom and the fact that new believers take the place of dead believers. It has been said that the blood of martyrs watered the seed of the gospel, and it is true that when people see faithful Christians die in faith, they are prompted to take that faith very seriously. Many have been "baptized for the dead", to take the place of the faithful who have died in the Lord. It is somewhat like what Paul said to the living but distant Philemon where the phrase "take your place" is actually the same Greek word as is translated "for" in "for the dead" of 1 Cor 15:29.

Philem 13 I would have liked to keep him with me so that he could take your place in helping me while I am in chains for the gospel. (NIV)

Consider also that in his last letter (2 Timothy) Paul was mindful of his own impending death in Rome when he reminded Timothy to make sure there were others to their places in the days and years ahead, new Christians and new leaders filling the gaps left by those who've died.

2 Tim 2:2 And the things you have heard me say in the presence of many witnesses entrust to reliable men who will also be qualified to teach others. (NIV)

And again, in Revelation John had a vision of the souls of martyrs under the altar crying out for justice, who were told to wait until the full number of those who would die for faith had been completed.

Rev 6:10-11 They called out in a loud voice, "How long, Sovereign Lord, holy and true, until you judge the inhabitants of the earth and avenge our blood?" 11 Then each of them was given a white robe, and they were told to wait a little longer, until the number of their fellow servants and brothers who were to be killed as they had been was completed. (NIV)

So, I would suggest three things that help understand Paul's statement about baptism for the dead. One is that the overall theme in 1 Cor 15 is the reality of the resurrection, not the doctrine or means or purpose of baptism. Those verses are about understanding the fundamental necessity of believing in the resurrection of both Jesus and all mankind. A second is that baptism is immutably bound together with the idea of dying to self and living for Christ. Christians formerly dead in sin are baptized into his death and raised to live with him. A third is that (in times of persecution especially) new believers take the place of believers who have died, until God's roll is completed and the resurrection does occur, and many have been motivated to be baptized because of the faithful stance of persecuted believers.

Hope this is helpful.