Repent ye (metanoēsate). First aorist (ingressive) active imperative. Change your mind and your life. Turn right about and do it now. You crucified this Jesus. Now crown him in your hearts as Lord and Christ. This first.
And be baptized every one of you (kai baptisthētō hekastos hūmōn). Rather, “And let each one of you be baptized.” Change of number from plural to singular and of person from second to third. This change marks a break in the thought here that the English translation does not preserve. The first thing to do is make a radical and complete change of heart and life. Then let each one be baptized after this change has taken place, and the act of baptism be performed “in the name of Jesus Christ” (en tōi onomati Iēsou Christou). In accordance with the command of Jesus in Mat 28:19 (eis to onoma). No distinction is to be insisted on between eis to onoma and en tōi onomati with baptizō since eis and en are really the same word in origin. In Act 10:48 en tōi onomati Iēsou Christou occurs, but eis to onoma in Act 8:16; Act 19:5. The use of onoma means in the name or with the authority of one as eis onoma prophētou (Mat 10:41) as a prophet, in the name of a prophet. In the Acts the full name of the Trinity does not occur in baptism as in Mat 28:19, but this does not show that it was not used. The name of Jesus Christ is the distinctive one in Christian baptism and really involves the Father and the Spirit. See note on Mat 28:19 for discussion of this point. “Luke does not give the form of words used in baptism by the Apostles, but merely states the fact that they baptized those who acknowledged Jesus as Messiah or as Lord” (Page).
Unto the remission of your sins (eis aphesin tōn hamartiōn hūmōn). This phrase is the subject of endless controversy as men look at it from the standpoint of sacramental or of evangelical theology. In themselves the words can express aim or purpose for that use of eis does exist as in 1Co 2:7 eis doxan hēmōn (for our glory). But then another usage exists which is just as good Greek as the use of eis for aim or purpose. It is seen in Mat 10:41 in three examples eis onoma prophētou, dikaiou, mathētou where it cannot be purpose or aim, but rather the basis or ground, on the basis of the name of prophet, righteous man, disciple, because one is, etc. It is seen again in Mat 12:41 about the preaching of Jonah (eis to kērugma Iōna). They repented because of (or at) the preaching of Jonah. The illustrations of both usages are numerous in the N.T. and the Koinéš generally (Robertson, Grammar, p. 592). One will decide the use here according as he believes that baptism is essential to the remission of sins or not. My view is decidedly against the idea that Peter, Paul, or any one in the New Testament taught baptism as essential to the remission of sins or the means of securing such remission. So I understand Peter to be urging baptism on each of them who had already turned (repented) and for it to be done in the name of Jesus Christ on the basis of the forgiveness of sins which they had already received.
The gift of the Holy Ghost (tēn dōrean tou hagiou pneumatos). The gift consists (Act 8:17) in the Holy Spirit (genitive of identification).