Source: Oliver Cowdery letter to W.W. Phelps in M&A l (Oct 1834):
After writing the account given of the Savior’s ministry to the remnant of the seed of Jacob, upon this continent, . . . it was as easily to be seen, that amid the great strife and noise concerning religion, none had authority from God to administer the ordinances of the gospel. . . .and we only waited for the commandment to be given, “Arise and be baptized.” This was not long desired before it was realized. . . After we had called upon him in a fervent manner, . . .the voice of the Redeemer spake peace to us, while the veil was parted and the angel of God came down clothed with glory, and delivered the anxiously looked for message, and the keys of the gospel of repentance!–What joy! what wonder! what amazement! . . . Then his voice, though mild, pierced to the center, and his words, “I am thy fellow servant,” dispelled every fear. We listened–we gazed–we admired! ‘Twas the voice of the angel from glory–’twas a message from the Most High! and as we heard we rejoiced, while his love enkindled upon our souls, and we were rapt in the vision of the Almighty! Where was room for doubt? No where: uncertainty had fled, doubt had sunk, no more to rise, while fiction and deception had fled forever! What joy filled our hearts . . .when we received under his hand the holy priesthood, as he said, “Upon you my fellow servants, in the name of Messiah I confer this priesthood and this authority, which shall remain upon earth, that the sons of Levi may yet offer an offering unto the Lord in righteousness!”
Source: Patriarch Blessing Book, 2 Oct 1835, cit. Joseph F. Smith, “Restoration of the Melchizedek Priesthood,” Improvement Era 7 (October 1904):942. [This statement by Oliver Cowdery was recorded under the date 2 October 1835 in the patriarchal blessing book of Joseph Smith, Sen., following one of the blessings. Oliver Cowdery was at that time the recorder.]:
He [Joseph Smith] was ministered unto by the angel, and by his direction he obtained the records of the Nephites, and translated by the gift and power of God. He was ordained by the angel John, unto the lesser or Aaronic priesthood, in company with myself, in the town of Harmony, Susquehanna County, Pennsylvania, on Friday, the 15th day of May, 1829; after which we repaired to the water, even to the Susquehanna River, and were baptized; he first administering unto me, and after, I to him. But before baptism our souls were drawn out in mighty prayer, to know how we might obtain the blessings of baptism and of the Holy Spirit according to the order of God; and we diligently sought for the right of the fathers, and the authority of the holy priesthood, and the power to administer the same; for we desired to be followers of righteousness, and in the possession of greater knowledge, even the knowledge of the mysteries of the kingdom of God. Therefore we repaired to the woods, even as our father Joseph said we should, that is, to the bush, and called upon the name of the Lord, and he answered us out of the heavens. And while we were in the heavenly vision, the angel came down and bestowed upon us this priesthood; and then, as I have said, we repaired to the water and were baptized. After this, we received the high and holy priesthood; but an account of this will be given elsewhere, or in another place.
Quote in the figure is from Joseph Smith—History 1:71-72.
“I laid my hands upon [Oliver’s] head and ordained him to the Aaronic Priesthood, and afterwards he laid his hands on me and ordained me to the same Priesthood—for so we were commanded…The messenger who visited us . . . said that his name was John”
Here is the complete verse 72:
“The messenger who visited us on this occasion and conferred this priesthood upon us said his name was John, the same that is called John the Baptist in the New Testament, and that he acted under the direction of Peter, James and John, who hold the Priesthood of Melchisedek, which Priesthood he said should in due time be conferred on us, and that I should be called the first elder and he the second. It was on the 15th day of 1829 that we were baptized, and ordained under the hand of the messenger.” JS-H 1:72