Restoration of the Aaronic Priesthood

Joseph Smith and Oliver Cowdery, while translating the Book of Mormon, both had a deep desire to understand how they could be baptized in order to receive salvation. They understood that they
needed to have the right authority from God to baptize them, but they did not know where that could be found. That is why they came together one day to the banks of the Susquehanna River and prayed to know how this truth could be made known unto them.
During this experience, John the Baptist (now a resurrected being) appeared to them and explained the first part of the Priesthood and the ordinances done with it. He helped them to understand just the very beginning of all they would learn about the priesthood. Then, he took his hands and put them on Joseph's head and then Oliver's head and ordained them to the Aaronic priesthood, giving them the power to baptize one another in Christ's name.
During this time they were just given the gift to baptize, but the baptism was not complete until they later received another priesthood to give them the ability to give the gift of the Holy Ghost to others.