Willard Richards summarizes details of the first endowment ceremony in Joseph's manuscript history of the Church.
Manuscript History of the Church, Draft, May 4, 1842, The Joseph Smith Papers website, accessed June 7, 2021
I spent the day in the upper part of the Store (IE.) in my private office (so called, because in that room I kept my the Sacred writings, an translated ancient records, and recseived revelation), and in my general business office. or Lodge room, <(ie where the masonic fraternity met occasionally for want of a better place)> in council with Gen James Adams, of Springfield, <patriar[c]h> Hyrum Smith, <bishop> Newel K. Whitney, <&> Geo. Miller, Wm Marks, WmLaw, & <& prests> Brigham Young Heber C. Kimball & Willard Richards, instructing them in the principles and order of the priesthood, attending to washings & anointings, & endowments, and the communication of keys, pertaining to the Aronic Priesthood, and so on to the highe[s]t order of the Melckisedec Pristhood, setting forth the order pertaining to the Ancient of days & all those plans & principles by which any one is enabled to secure the fulness of those blessings which has <been> prepared for the chuch of the first-born, and come up, into and abide in the [presence] of God in the Eloheim in the eternal worlds. In this council was instituted the Ancient order of thinks things <for, the fi[r]st time> in these last days.— And the communication I made to these this council <of this council> woere of things Spiritul, and to be received only by the spiritual Minded; and there was nothing made known to these men but what will be made known to all Saints, of the last days, so soon as they are prepared to receive, them, once a proper place is prepared to communicate them, even to the weakest of the Saints; therefore let the saints be diligent in building the Temple and all houses which they have been or shall hereafter be commanded of God to build, and wait their time with patience, in all meekness faith, & perseverance unto the end, knowing assuredly that all these things refered to in this council are always governed by the principles of Revelation.
Although the account is written in the first person, the detailed summary of the endowment should be attributed to Willard Richards, not Joseph Smith (see Joseph Smith, Jr., Andrew H. Hedges, Alex D. Smith, and Richard Lloyd Anderson. Journals: December 1841-April 1843. The Joseph Smith Papers, Journals 2, ed. Dean C. Jessee, Ronald K. Esplin and Richard Lyman Bushman. Salt Lake City, UT: The Church Historian's Press, 2011, 55n198, https://www.josephsmithpapers.org/paper-summary/journal-december-1841-december-1842/25#XD52912FA-2D4A-4219-B222-C13161B258DB ).