Question:Can you discuss the exchange that takes place between a preacher (or the person baptizing)†and the one being baptized. What exactly should be said in this exchange? I have convinced a neighbor that his baptism is not scriptural and he would like to be baptized according to God's word.
I'm not certain exactly what you are asking. Whenever a preacher finds someone interested in being a Christian, he tries to establish where a person is at in his understanding of salvation and direct him toward where he needs to go. If you go through Acts you will find that as people become convicted of their need to be saved, that different answers are given depending on where the person is currently at.
"Now when they heard this, they were cut to the heart, and said to Peter and the rest of the apostles, "Men and brethren, what shall we do?" Then Peter said to them, "Repent, and let every one of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit" (Acts 2:37-38).
These people believed because they asked what they needed to do. Thus Peter told them they needed to change and be baptized. When the Ethiopian eunuch wanted to understand a passage in Isaiah:
"So the eunuch answered Philip and said, "I ask you, of whom does the prophet say this, of himself or of some other man?" Then Philip opened his mouth, and beginning at this Scripture, preached Jesus to him. Now as they went down the road, they came to some water. And the eunuch said, "See, here is water. What hinders me from being baptized?" Then Philip said, "If you believe with all your heart, you may." And he answered and said, "I believe that Jesus Christ is the Son of God." So he commanded the chariot to stand still. And both Philip and the eunuch went down into the water, and he baptized him" (Acts 8:34-38).
The eunuch needed more background so that he might have faith in Jesus, which Philip supplied by teaching him about Jesus. That teaching had to have included baptism because the eunuch is the one who brought up the topic when he saw water nearby.
Take a look at the chart "Conversions" and see that every case of conversion was unique because each individual started with a different level of knowledge and accomplishments.
As far as what to say during a baptism, the words of Jesus in Matthew 28:19-20, Peter's in Acts 2:38, Philip's in Acts 8:37, or Ananias' in Acts 22:16 are obviously satisfactory. Most preachers I know blend the ideas together.