Moroni gives us the formula used to confer the priesthood. The basic formula remains the same today. The medium through which the power may be transmitted is declared to be Jesus Christ. His is the name that makes the ordinance effective. After declaring the authority by which the action is done, the administrator declares what is being done.
The person is ordained to the specific calling that they will fulfill. At this point in the Nephite record we do not have any indication of a knowledge of the difference between the Aaronic and the Melchizedek priesthoods. They may have known of such a division, but there is no textual evidence to clearly indicate that division. In this case, the position is emphasized more than the priesthood. This would seem to indicate that in Nephite practice, as in earliest Christian practice, the priesthood was reserved for officiators. One received the calling to do something, and that calling was equipped with the authority (priesthood) to perform it.
After the person receives the specific calling, he is given an admonition concerning that calling. In modern practice, this is where the unique blessing is given to the individual for the performance of their calling. In Moroni, the calling is genericized into the formulaic statement: “to preach repentance and remission of sins through Jesus Christ, by the endurance of faith on his name to the end.” Given the definition of the gospel in the Book of Mormon (DC 39:6) this would simply be an admonition to preach the gospel. This should not be seen as a missionary call, but rather a call to be in a particular relationship to those in the church who have not the callings to be priest of teacher.
The conclusion of the verbal statement is the word Amen. The usage of this term is so well attested in the Bible that it was certainly part of Joseph’s understanding. That conclusion is absolutely appropriate, but it may or may not have been the specific closing statement of the Nephites (even though it harkened to their Hebrew past). We simply cannot know.