I am borrowing generously from websites for which I will provide links to below. The following is from: http://www.mormoninformation.com/srtheory.htm
The "Spalding-Rigdon theory" was first given wide publicity in 1834 with the publication of the book Mormonism Unvailed. In it, the author followed up on indications previously published in Ohio-based newspapers that a man named Solomon Spalding was the real (and unwitting) originator of the Book of Mormon.
To make an extremely long story very, very short, the theory goes that Solomon Spalding authored a work called "Manuscript Found" (not to be confused with "Manuscript Story"!)...Supposedly Sidney Rigdon, who actually lived nearby and would later become Joseph Smith's right-hand man, was acquainted with the publisher. Rigdon procured Spalding's manuscript, edited it by inserting a great deal of religious material, and later turned it over to Joseph Smith who then used it, and not any golden plates, as full or partial source material for the Book of Mormon.
The Spalding document described in Mormonism Unvailed was rediscovered in Hawaii in 1884, but it was shown to be far from the expected word-for-word parallel to the Book of Mormon, so the theory went into hiatus. The theory went into virtual moratorium in 1945 with the publication of Fawn M. Brodie's No Man Knows My History. Although considered by Mormons as an anti-Mormon book, she rejected the "Spalding-Rigdon theory" of Book of Mormon authorship due in part to her documentation of Rigdon's activities at the time which supposedly proved that Rigdon never met Joseph Smith until after the Book of Mormon was published. She had, however, imported this information wholesale from a pro-LDS source and had done little, if any, of her own research into the matter. There are also significant gaps in the chronology.
Although the Spalding-Rigdon theory was on the back burner for over half a century, in July 2005 the book Who Really Wrote the Book of Mormon? The Spalding Enigma hit the shelves. It contains a great amount of brand-new evidence and will very likely bring the Spalding-Rigdon controversy back to "front and center."
Many apologists love to show how "Manuscript Story" does not have much in common with the BoM and does not contain BoM names as many witnesses had attested that a manuscript of Spalding's did. And many proponents of the Spalding-Rigdon theory have demonstrated the many parallels exist in wording between "Manuscript Story" and the BoM. But, the evidence suggests that there were two books that Spalding wrote, one entitled "Manuscript Found" about Hebrews who sailed to America, and another earlier book entitled "Manuscript Story: Conneaut Creek" about a small group of Romans who were blown off course and landed in America. To add to the confusion the RLDS published the Hawaiian copy of "Manuscript Story" under the name of "Manuscript Found" apparently because they believed the book they had was the same one that the affidavits spoke of. One cannot entirely blame them because the confusion appears to have started in "Mormonism Unveiled".
Apparently a man by the name of Hurlbut collected several affidavits from individuals who knew Spalding and had heard him read parts of "Manuscript Found" to them. They claimed that there were many similarities between Spalding's book and the Book of Mormon except that the BoM had many scriptural teachings which were not in Spalding's book. E. D. Howe, the author of "Mormonism Unveiled" heard of these affidavits and went to Spalding's relatives to see if the claims in the affidavits were true (Solomon Spalding was dead). Howe ended up leaving the Spalding household with "Manuscript Story" thinking he had found what he was looking for. But, upon examining it found that it did not bear the strong resemblance to the BoM he was expecting. His copy was lost after he died and then found in Hawaii. The RLDS church correctly believed that it was the same manuscript Howe had, but incorrectly believed as Howe had that it was the one that was referred to in the affidavits. The RLDS wanted to show that the BoM was not a fraud and was not similar to the Spalding book, so they published the copy of "Manuscript Story" they had as "Manuscript Found".
A daughter of Spalding said that "Manuscript Story: Conneaut Creek" was not the same as "Manuscript Found" (http://www.mormonstudies.com/matilda1.htm):
In her 1880 statement, Mrs. McKinstry stated that after Solomon died in 1816, his writings were stored in a trunk: "I perfectly remember the appearance of this trunk, and of looking at its contents. There were sermons and other papers, and I saw a manuscript, about an inch thick, closely written, tied with some of the stories my father had written for me, one of which he called, 'The Frogs of Wyndham.' On the outside of this manuscript were written the words, 'Manuscript Found.' I did not read it, but looked through it and had it in my hands many times, and saw the names I had heard at Conneaut, when my father read it to his friends. I was about eleven years of age at this time" (Cowdrey et al. 1977, 52-53)
Matilda was also just as clear about the fact that her father's manuscript, which contained the names Mormon, Maroni, Lamenite, and Nephi, bore the title "Manuscript Found," not "Manuscript Story." In a letter to James Fairchild dated 18 February 1886, A. B. Deming wrote: "I was in Washington D.C. 10 days Dec. and Jan. and gave Spaulding's daughter L. L. Rice's Story as Pub[lished] at Lamoni. She says it is not Manuscript Found." This was confirmed by Matilda in a letter to Deming in November 1886: "I have read much of the Manuscript Story Conneaut Creek which you sent me. I know that it is not the Manuscript Found which contained the words 'Nephi, Mormon, Maroni, and Laminites.' Do the Mormons expect to deceive the public by leaving off the title page - Conneaut Creek - and calling it Manuscript Found and Manuscript Story?" (See Cowdrey et al. 1977, 157-58.)
These letters written by A. B. Deming and Mrs. McKinstry assume even more significance when compared to another letter dated 25 January 1886 from Redick McKee to Deming. McKee's letter begins with this sentence: "When in this city a few days ago, you informed me that you were en route to Pittsburg, Washington County, &c, to collect some additional testimony about the origin of the Mormon Bible for a book you were intending to publish on this subject, that you had seen old Mrs. McKinstry - the daughter of Solomon Spaulding - and obtained a statement of her recollections and now called to request a similar statement from me, to include incidents of my early and later life, leading to my present matured opinion about Mormonism." After relating what he knew of Solomon Spalding while living at Spalding's public house in Amity between 1814 and 1816, McKee provided this information:
But touching these I will give below his daughter's (Mrs. McKinstry's) recollections, recently narrated by her to me, which I think more full and explanatory than my own. This lady is still residing in Washington, D.C., with the family of her late son-in-law, Col. Seaton of the Census Bureau, in remarkably good health for a lady of her age. She corroborated her father's statement about his removal to Conneaut in 1809, his examining the Indian mounds &c, and distinctly recollected that he wrote two or more stories in support of the theory that the Indians of North America were lineal descendants of the Jews from Palestine. In the first of these he brought the Jews from Palestine to America via Italy during the reign of Constantine, and set forth that at Rome they engaged shipping to convey them to some place in Great Britain, but encountered stormy weather and were finally wrecked somewhere on the coast of New England. What became of the manuscript of this story she did not know with certainty but understood that it was published in some Eastern review or magazine.
This romance he afterwards abandoned and set about writing a more probable story founded on the history of the ten lost tribes of Israel. She thought her father must have had wonderful powers of imagination and memory, great command of language and facility of description. Many of his descriptions were of a historical and religious character. Others were grotesque and ludicrous in the extreme.
She remembered that in one of them, touching the mode of warfare in that day, (being hand to hand or man to man) he represented one of the parties having streaks of red paint upon their cheeks and foreheads to distinguish them from enemies in battle. The story he called "The Manuscript Found." It purported to give a history of the ten tribes, their disputes and dissentions concerning the religion of their fathers, their division into two parties; one called Nephites the other Lamanites; their bloody wars, followed by reunion and migration via the Red Sea to the Pacific Ocean; their residence for a long time in China; their crossing the ocean by Behrings Straits in North America, thus becoming the progenitors of the Indians who have inhabited or now live in this continent. This was the story which her uncle John, Mr. Lake, Mr. Miller and other neighbors heard him read at Conneaut on different occasions. (Cowdrey et al. 2000, 798-99)
You can read "Manuscript Story" which was incorrectly published as "Manuscript Found" here.
To read the statements made by those who heard Solomon Spalding's "Manuscript Found" look here: http://www.solomonspalding.com/docs/1834howf.htm#pg278b
In addition to reading all of the above links, please be sure to read: http://sidneyrigdon.com/criddle/rigdon1.htm and http://sidneyrigdon.com/criddle/rigdon2.htm