The baptism should be performed by a priest of the Aaronic priesthood or a holder of the higher priesthood. Baptism is required for several reasons. First, it is an outward sign of one's acceptance of Jesus Christ as personal Savior and the public confession before the church of having repented of sins, having the resolve to obey the Lord's commandments (D&C 20:37). Second, it is a public acknowledgement of one's acceptance of the man performing the baptism being an authorized servant of the Lord. This was the reason Jesus was baptized by John the Baptist. John held the keys of his short dispensation which he wrested from the Jews. Finally, it is often required at the beginning of a new dispensation, which applies in this case.
The baptismal prayer used is that prescribed in the Doctrine and Covenants (D&C 20:73). There should be two witnesses if possible, which may be male or female of age 8 or more, and need not be members of the Church. The best may be priesthood holders who have memorized the prayer to witness that it was said correctly.
If any one witness states that the immersion was not complete, then only the immersion need be repeated, not the prayer.