In the Book of Mormon, it was the priest who was assigned to preach the word:
19 And it came to pass that king Mosiah granted unto Alma that he might establish churches throughout all the land of Zarahemla; and gave him power to ordain priests and teachers over every church.
20 Now this was done because there were so many people that they could not all be governed by one teacher; neither could they all hear the word of God in one assembly;
21 Therefore they did assemble themselves together in different bodies, being called churches; every church having their priests and their teachers, and every priest preaching the word according as it was delivered to him by the mouth of Alma. (Mosiah 25: 19-21)
Baptisms
13 And Alma established a church in the land of Sidom, and consecrated priests and teachers in the land, to baptize unto the Lord whosoever were desirous to be baptized. (Alma 15:13)
Communion
1 The manner of their elders and priests administering the flesh and blood of Christ unto the church; and they administered it according to the commandments of Christ; wherefore we know the manner to be true; and the elder or priest did minister it— (Moroni 4:1)
Every 50, Preach, Teach, Finances
18 And it came to pass that Alma, having authority from God, ordained priests; even one priest to every fifty of their number did he ordain to preach unto them, and to teach them concerning the things pertaining to the kingdom of God.
19 And he commanded them that they should teach nothing save it were the things which he had taught, and which had been spoken by the mouth of the holy prophets.
20 Yea, even he commanded them that they should preach nothing save it were repentance and faith on the Lord, who had redeemed his people.
21 And he commanded them that there should be no contention one with another, but that they should look forward with one eye, having one faith and one baptism, having their hearts knit together in unity and in love one towards another.
22 And thus he commanded them to preach. And thus they became the children of God.
23 And he commanded them that they should observe the sabbath day, and keep it holy, and also every day they should give thanks to the Lord their God.
24 And he also commanded them that the priests whom he had ordained should labor with their own hands for their support.
25 And there was one day in every week that was set apart that they should gather themselves together to teach the people, and to worship the Lord their God, and also, as often as it was in their power, to assemble themselves together.
26 And the priests were not to depend upon the people for their support; but for their labor they were to receive the grace of God, that they might wax strong in the Spirit, having the knowledge of God, that they might teach with power and authority from God.
27 And again Alma commanded that the people of the church should impart of their substance, every one according to that which he had; if he have more abundantly he should impart more abundantly; and of him that had but little, but little should be required; and to him that had not should be given.
28 And thus they should impart of their substance of their own free will and good desires towards God, and to those priests that stood in need, yea, and to every needy, naked soul.
29 And this he said unto them, having been commanded of God; and they did walk uprightly before God, imparting to one another both temporally and spiritually according to their needs and their wants. (Mosiah 18)