Paul is very clear in Romans chapter 6 that baptism is a participation in Christ’s death and resurrection. So, this cleansing is being symbolised, but there’s also a new life—that’s where the resurrection element comes in.
When you are baptised, you’re being shown that you have a new life empowered by the Spirit. Essentially, you see that in Ephesians chapter 4 too: “There is one body and one Spirit, one Lord, one faith, one baptism, one God and Father of all,” says Paul. So the stress is on the unity of the Trinity in the Christian life, which baptism inaugurates.
It’s the same in 1 Corinthians 12 and 13. What were all the believers in Corinth baptised by, or rather, who were all the believers in Corinth baptised by? Paul says one Spirit, so as to form one body—whether Jew or Gentile, slave or free—and we’re all given the one Spirit to drink.
So, in those two sacraments—baptism and the Lord’s Supper—it is the Holy Spirit who is involved. That was the emphasis of the apostles here in Acts 8, and it has just been the emphasis of the church ever since.
This is quite a common story amongst young people nowadays—that they have sought to live the Christian life, but they’ve never been baptised. That’s wrong too, because baptism is so diminished in our day and age.