The Church of Christ incorporated according to the laws of the New York. The traditional site for this meeting is the Peter Whitmer, Sr., log house in Fayette, New York. However, there is also evidence that the meeting may have taken place in the old Smith family log cabin in Manchester, New York.
Six men were the incorporators. No minutes of the meeting exists and a variety of lists of these men have appeared. The earliest list (1833) gives the names of Joseph Smith, Jr., Oliver Cowdery, Joseph Knight, Hyrum Smith, Joseph Smith, Sr., and Samuel Smith. A later list  by David Whitmer gives Joseph Smith, Jr., Oliver Cowdery, Hyrum Smith, David Whitmer, Christian Whitmer and John Whitmer. In other lists Whitmer includes Martin Harris and Peter Whitmer, while omitting Christian and John Whitmer. Without minutes or the incorporation papers the identity of the six men cannot be precisely determined.
There were persons others present. David Whitmer wrote that there were "about 20 from Colesville, 15 from Manchester Church and about 20 from around Father Whitmers". This figure is probably inflated, because the minutes of the Church's second conference, 26 Sept. 1830, give the total Church membership as sixty-two, with thirty-five of those having been baptized between 9 June and 26 Sept. 1830.
Joseph Smith and Oliver Cowdery ordained each other elders. Other men were also ordained elders. Oliver also ordained Joseph as a prophet, seer and revelator. The Sacrament was passed, and baptisms and confirmations were performed. Later Joseph and Oliver's ordinations were refined to reflect the two men's position in the priesthood hierarchy: Joseph Smith became "first elder" and Oliver Cowdery "second elder." (Book of Commandments  refers to both men as elders [Chap. XXIV, vss. 3-4], but in the Doctrine and Covenants  the text was changed to "first elder" and "second elder." [Sect. 2, vs. 1])
[Lisle G Brown, compiler, "Organizational Chronology of The Church of Christ, and The Church of the Latter Day Saints, 1829 - 1836"]