I offer a brief summary of what we know of the Book of Mormon "translation" process. I welcome corrections if anyone is aware of any. There are a number of articles that have been written on the subject, all of which are in substantive agreement (Refs follow commentary).
After reviewing the accounts from Joseph Smith (1838, 1842), Emma Smith Bidamon (1870, 1879), David Whitmer (1875, 1879, 1881, 1885, 1886, 1887), Oliver Cowdery (1834, 1859), Martin Harris (1882), Elizabeth Ann Whitmer Cowdery Johnson (1870), Michael Morse (1879), Isaac Hale (1834), Alva Hale (1834), William Smith (1883, 1884, 1891), and neighbors of Joseph Smith collected in 1833 by Dr. Philatus Hurlburt, -- James E. Lancaster provides this summary:
"An examination of the foregoing eyewitness testimonies produces the following consensus on the method of translation of the Book of Mormon:It is interesting to note that in a 25 June 1992 seminar for new mission presidents, Elder Russell M. Nelson said, "The details of this miraculous method of translation are still not fully known. Yet we do have a few precious insights." (Ensign, July 1993, p. 62.) Then he quoted from David Whitmer's 1887 account in which Joseph Smith "would put the seer stone into a hat, and put his face in the hat...."
(1) Nephite interpreters often called "Urim and Thummim" were found with the plates on Hill Cumorah; [my note: The words "Urim and Thummim" were never used to describe the stones until after the Book of Mormon was published. Even then the term was first used by people other than Joseph Smith.]
(2) these interpreters were used first in the translation of the plates;
(3) the portion translated by use of the interpreters was copied into 116 pages of foolscap and was later lost by Martin Harris;
(4) because of the loss of the first 116 pages of translation, the interpreters were permanently taken away [June/July 1828];
(5) the Book of Mormon that we have today was translated by use of the seer stone;
(6) Smith translated by placing the seer stone in a hat and covering his face with his hat to darken his eyes;
(7) the plates were not used in the translating process and often were not even in sight during the translation;
(8) other persons were sometimes in the room while Smith dictated to a scribe; and
(9) [almost] all witnesses agree to these facts.
The earliest newspaper accounts do not differ significantly from this scenario." ("The Translation of the Book of Mormon", pp. 105-6)
Several witnesses claimed that Smith saw English words or letters appear before his eyes. However, other statements by some of the same men, other witnesses, and revelations (D&C 8,9) infer the translation process was not automatic and mechanical. Supporting this are the thousands of corrections and textual revisions made to the original manuscript by Joseph Smith. The third or 1840 edition of the Book of Mormon was printed with this statement, "Carefully Revised by the Translator." B.H. Roberts concluded,
"The translation of the Book of Mormon by means of the "Interpreters" and "Seer Stone," was not merely a mechanical process, but required the utmost concentration of mental and spiritual force possessed by the prophet..." (Young Men's Manual, 1903-4, p. 69)It is also clear that when Joseph Smith came to Biblical material in the Nephite record, he simply adopted it from the KJV of the Bible, making changes as he saw fit. Finally, revelations received by Joseph Smith up to June 1829 were received through the seer stone (some D&C section prefaces (added much later) use the words "Urim and Thummim"), but Joseph Smith authorized numerous changes in both wording and content here also.
"This view of the translation of the Nephite record accounts for the fact that the Book of Mormon, though a translation of an ancient record, is nevertheless, given in English idiom of the period and locality in which the prophet lived; and in the faulty English, moreover as to composition, phraseology, and grammar, of a person of Joseph Smith's limited education; and also accounts for the sameness of phraseology and literary style which runs through the whole volume." (Young Men's Manual, 1903-4, p. 71)
Joseph Smith mentioned several times that he translated the Book of Mormon record through the gift and power of God by means of the "Urim and Thummim", but the term was used ambiguously. The words "Urim and Thummim" did not appear in the Book of Mormon, early revelations, or early newspaper accounts. The first time the U&T was used to refer to the Nephite interpreters was in 1833 when W.W. Phelps equated them in the first edition of the Evening and Morning Star. By 1835 the term was added to the revelation published as D&C 10 (verse 1), and thereafter, was used to refer to both the Nephite interpreters and the seer stone(s) by Joseph Smith and numerous other people. David Whitmer's accounts of the "Urim and Thummim" or "interpreters" put in a hat had to refer to Joseph Smith's seer stone as he didn't meet Joseph until June 1829, a year after the "interpreters" were taken from Joseph Smith. The same goes for Oliver Cowdery's use of the terms in his description of the translation process. He moved in with the Smiths in the winter of 1828 to act as scribe for Joseph Smith.
James E. Lancaster, "8. The Translation of the Book of Mormon", from Dan Vogel, ed., The Word of God: Essays on Mormon Scripture, pp. 97-112.
Richard Van Wagoner and Steve Walker, "Joseph Smith: 'The Gift of Seeing' Dialogue, Vol 15, No. 2, pp. 49-68.
Paul E. Dahl, "Theories of the Origin, Translation Process and Publication of the Book of Mormon," unpublished 1982 paper. Paul was a LDS Institute Director and a Stake President at the time.