First, the ideas in the book of mormon aren't this radical and original thing. Before and around Jospeh's time there were ideas about the Native Americans and stories going around about the early americas. I don't doubt these held some inspiration for the "prophet" Joseph's work.
Some evidence of these ideas can be seen in many places. The idea of linking the native american people to the tribes of Israel wasn't one that originated with Joseph. There were many books written about the ancient americans. For instance a book called View of the Hebrews:
"The probability then is this; that the ten tribes arriving in this continent with some knowledge of the arts of civilized life, finding themselves in the vast wilderness filled with the best of game inviting them to the chase, most of them fell into a wandering idle hunting life. Different clans parted from each other, lost each other, and formed the separate tribes. Most of them formed a habit of this idle form of living and were pleased with it.
More sensible parts of this people associated together to improve their knowledge of the arts and probably continued thus for ages. From these the noted relics of civilization discovered in the west and south were furnished. But the savage tribes prevailed; and in process of time their savage jealousies and rage annihilated their more civilized brethren. And thus as a wholly vindictive providence would have it, and according to ancient denunciations all were left in an 'outcast' state. This accounts for their loss of their knowledge of letters, of the art of navigation and of the use of iron, and such a loss can no more operate against their being the ten tribes, then against their being of any other origin.
It is highly probable that the more civilized part of the tribes of Israel after they settled in America became wholly separated from the hunting and savage tribes of their brethren; that the latter lost the knowledge of their having descended from the same family with themselves; that the more civilized part continued for many centuries, that tremendous wars were frequent between them and their savage brethren until the former became extinct." (Ethan Smith - View of the Hebrews - 1825(second edition), 172-73) (The book was first published in 1823)
The resemblance to the Book of Mormon story is rather uncanny! Many similarities can be found between both books.
But this wasn't the only book expressing the relation of the tribes of Israel to the native Americans. More examples:
Elias Boudinot's book A Star in the West; or a humble attempt to discover the long lost Ten Tribes of Israel, preparatory to their return to their beloved city, Jerusalem (1816)
James Adair's book The History of the American Indians (1775)
Charles Crawford's book An Essay upon the Propagation of the Gospel, in which there are facts to prove that many of the Indians in America are descended from the Ten Tribes (1799)
Josiah Priest's book The Wonders of Nature and Providence Displayed (1825)
Because of the excitement over the Native American's origins and connections to the ten tribes it isn't too hard to see where Joseph got some ideas from.
Is it possible that Joseph was exposed to some of these books? B.H. Roberts thought that that it was very likely that Joseph had access to View Of the Hebrews:
"...did Ethan Smith's View of the Hebrews furnish structural material for Joseph Smith's Book of Mormon? It has been pointed out in these pages that there are many things in the former book that might well have suggested many major things in the other. Not a few things merely, one or two, or a half dozen, but many; and it is this fact of many things of similarity and the cumulative force of them that makes them so serious a menace to Joseph Smith's story of the Book of Mormon's origin ...
The material in Ethan Smith's book is of a character and quantity to make a ground plan for the Book of Mormon ...
Can such numerous and startling points of resemblance and suggestive contact be merely coincidence?"
(B.H. Roberts - Studies of the Book of Mormon - pages 240, 242)
At the very least it is absolutely clear that the ideas of the book of mormon came from other places. The popular myths going around in Joseph's time show that Joseph certainly had inspiration for the Book of Mormon from the ideas around him.
There is also the extremely interesting Spalding Manuscript theories. I might write something on that later.
I don't completely subscribe to any theory as of yet. I do know that there is a lot of evidence that Joseph wasn't just an uneducated farm boy without the means or motive to create the book of mormon. I am doubtful that he made up the book on his own, but I don't think it was given to him by god or an angel. I believe he took the ideas from the mythology around him and he and his friends likely worked together on creating the book.
Besides that there are many examples of simple or uneducated people doing rather marvelous things. Even writing books. For instance, we have the uneducated and illiterate prophet Mohammed who wrote the Quran/Koran.