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The Book of Mormon runs to something over five hundred pages in a modern edition. The part of the work people usually mean when they say "the translation" took about three months.
The short answer
Oliver Cowdery began writing on 7 April 1829. The manuscript was finished by the end of June that year.
That is roughly eighty-five days from start to finish, and fewer once you take out sabbaths, travel, and the days spent on other things. Most counts put the actual working days somewhere around sixty-five.
The wider story runs from September 1827 to March 1830, and most of that stretch is not translation at all. It is waiting, interruption, and printing.
From the plates to the first scribe
Joseph Smith received the plates on 22 September 1827, at the hill near Manchester, New York, after four years of yearly visits.
What followed was not a productive winter. Attempts to get at the record and read it drew attention, and attention in Manchester meant people trying to take it. By December the Smiths had moved to Harmony, Pennsylvania, to Emma's family, largely to be somewhere quieter.
Work through that winter was slow and intermittent. Emma acted as scribe for a time. Her brother Reuben Hale did some. Joseph copied characters from the plates onto a sheet, which Martin Harris took to New York to show to scholars — the episode that produced the exchange with Charles Anthon.
Martin Harris and the lost pages
Martin Harris arrived in Harmony in April 1828 and worked as scribe through to June. Between them they produced 116 pages of manuscript, covering the book of Lehi.
Harris asked repeatedly to be allowed to take the pages home to show his family. After three askings he was permitted to, under strict conditions about who could see them. They were lost, and never recovered.
The consequences were immediate. Joseph lost the gift and the plates for a period. When the work resumed, it resumed without Harris.
The lost pages are the reason the translation has two distinct phases with a long gap between them, and the reason the finished book has the structure it does.
The gap
From the summer of 1828 to the spring of 1829, almost nothing happened. There are a few days of work with Emma scribing early in 1829. Otherwise the manuscript sat where the loss had left it.
Nine months of a twenty-two month story is this gap. It is worth holding on to, because the usual telling compresses everything into a single burst of activity and it was not one.
Oliver Cowdery arrives
Oliver Cowdery was a schoolteacher boarding with the Smith family in Manchester, which is how he heard about the plates. He travelled to Harmony and arrived on 5 April 1829.
Two days later, on 7 April, they began. From that point the work is continuous and fast.
At the end of May or beginning of June the two of them moved to the Peter Whitmer farm at Fayette, New York, to escape harassment at Harmony and to finish in peace. They finished there before the end of June.
On 11 June 1829 Joseph secured the copyright, which means enough of the text existed by then to register the title page — itself translated from the last leaf of the plates.
The pace
Set out plainly, the working rate is the thing most people find hardest to take in.
Something in the region of five hundred printed pages, in around sixty-five working days, is roughly seven or eight printed pages a day, dictated aloud, without notes, without a draft, and without going back to revise.
The original manuscript is largely free of the kind of corrections a composing author leaves. There is scribal correction — misheard words, spelling, punctuation added later — but very little evidence of an author changing his mind about content.
Witnesses on both sides of the question described the same method: Joseph dictating, the scribe writing and reading back, the plates themselves not being consulted in the way one might expect of a translator working from a text.
What that means is a matter of belief and always has been. What the record shows is the pace, and the pace is not in serious dispute.
The order is not the order you read
This is the detail that most rewards knowing.
The 1829 work did not start at the beginning of the book. It picked up where the lost pages had ended, at Mosiah, and ran forward through Alma, Helaman, Third Nephi, Fourth Nephi, Mormon, Ether and Moroni to the end.
Only then did Joseph translate the small plates of Nephi — First and Second Nephi, Jacob, Enos, Jarom and Omni — which now stand at the front of the book.
So the first hundred and forty pages a reader meets were the last hundred and forty translated. They were translated to replace what Harris had lost, and the book carries an explanation of the substitution in the Words of Mormon.
Anyone reading the book in the order it was produced starts at Mosiah. It is an unusual way in, and it makes the small plates read very differently when you reach them.
Then the slow part
Translation took three months. Printing took eight.
Egbert B. Grandin of Palmyra agreed to print five thousand copies for three thousand dollars, with Martin Harris mortgaging his farm to secure it. Typesetting began in August 1829 and ran to March 1830.
The compositor, John Gilbert, worked from a copy of the manuscript rather than the original, and added the punctuation, which the manuscript largely lacks.
The book went on sale on 26 March 1830, eleven days before the Church was organised.
Two and a half years from the hill to the bookshop. Three months of it was the translation.
The whole decade is laid out in the Restoration decade, 1820 to 1830, in order, and the events are on the timeline under the Book of Mormon translation filter.