After the Prophet Joseph Smith and Oliver Cowdery received the Aaronic Priesthood, the Prophet Joseph recorded that John the Baptist told them:
This Aaronic Priesthood had not the power of laying on hands for the gift of the Holy Ghost, but that this should be conferred on us hereafter.
[Oliver Cowdery and I] now became anxious to have that promise realized … , that provided we continued faithful, we should also have the Melchizedek Priesthood, which holds the authority of the laying on of hands for the gift of the Holy Ghost. We had for some time made this matter a subject of humble prayer.
The exact date and place where Joseph Smith and Oliver Cowdery received the Melchizedek Priesthood is unknown. What is known is that Peter, James, and John, Apostles of Jesus Christ, conferred upon the Prophet Joseph Smith and Oliver Cowdery the keys and authority of the Melchizedek Priesthood. They now had the power and authority necessary to organize The Church of Jesus Christ of Latter-day Saints, which the Lord commanded them to do on April 6, 1830.
We met together … on Tuesday, the sixth day of April, A. D., one thousand eight hundred and thirty. Having opened the meeting by solemn prayer to our Heavenly Father, we … call[ed] on our brethren to know whether they accepted [myself and Oliver Cowdery] as their teachers in the things of the Kingdom of God, and whether … we should proceed and be organized as a Church according to [the] commandment which we had received. To these several propositions they consented by a unanimous vote. I then laid my hands upon Oliver Cowdery, and ordained him an Elder of the “Church of Jesus Christ of Latter-day Saints;” after which, he ordained me also to the office of an Elder of said Church. … We then laid our hands on each individual member of the Church present, that they might receive the gift of the Holy Ghost, and be confirmed members of the Church of Christ. The Holy Ghost was poured out upon us to a very great degree.
We now proceeded to … ordain some others of the brethren to different offices of the Priesthood, according as the Spirit manifested unto us: and after … feeling for ourselves the powers and blessings of the Holy Ghost, … we dismissed with the pleasing knowledge that we were now … organized in accordance with commandments and revelations given by [God]. … Several persons who had attended the above meeting, became convinced of the truth and came forward shortly after, and were received into the Church; among the rest, my own father and mother were baptized, to my great joy and consolation.
(See History of the Church 1:39, 60, 75–79.)