Acts 2:31-32 (RSV) “he [David] foresaw and spoke of the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption.  This Jesus God raised up, and of that we all are witnesses.” (cf. 2:24).
Acts 2:33-34, 36 “exalted at the right hand of God, . . .  For David did not ascend into the heavens; but he himself says, `The Lord said to my Lord, Sit at my right hand, . . .  Let all the house of Israel therefore know assuredly that God has made him both Lord and Christ, . . .”
Acts 2:37 Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brethren, what shall we do?”
Acts 2:38-41 And Peter said to them, “Repent, and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins; and you shall receive the gift of the Holy Spirit.  For the promise is to you and to your children and to all that are far off, every one whom the Lord our God calls to him.”  And he testified with many other words and exhorted them, saying, “Save yourselves from this crooked generation.”  So those who received his word were baptized, and there were added that day about three thousand souls.
The first thing Peter says, is to “repent”: which is no different from any Protestant evangelist. If a person doesn’t repent, they can’t receive what God has for them. Then what’s next? The “sinner’s prayer”? Reciting of a Bible verse? Having folks pray over the repentant sinner up in the front of the church? No. What’s next is baptism. This was precisely the first thing the Apostle Paul did, too, when he had a change of heart and converted to Christ (Acts 9:18; 22:16), with the immediate result being a filling of the Holy Spirit (Acts 9:17) and a washing away of sins (Acts 22:16).
This is precisely what we see in Acts 2 above. Baptism brings about “forgiveness of . . . sins” and reception of “the gift of the Holy Spirit” (2:38). And it saves (i.e., regenerates) them, since Peter urged them to “save yourselves”: which they accomplished by being baptized. Peter elsewhere reiterates the same thing by stating that baptism “saves you, . . . through the resurrection of Jesus Christ,” (1 Pet 3:21), and draws the parallel of the eight persons in Noah’s ark, who were “saved through water” (1 Pet 3:20).
Acts 2:41, 47 So those who received his word were baptized, and there were added that day about three thousand souls. . . .  . . . And the Lord added to their number day by day those who were being saved. (cf. 5:14: “believers were added to the Lord” and 11:24: “a large company was added to the Lord”)
1 Peter 1:9 As the outcome of your faith you obtain the salvation of your souls.*1 Peter 3:18 For Christ also died for sins once for all, the righteous for the unrighteous, that he might bring us to God . . . [followed by baptism as the means of this salvation: 3:21]
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Summary: How does a Christian go about evangelizing and saving souls? The Bible (perhaps surprisingly to many) places baptism right in the center of this process.