In a nutshell -
In the Book of Mormon, a prophet known as Lehi was told to take his family and flee because Jerusalem was about to be destroyed. His family eventually built boats, and in time they wound up in the New World. Unfortunately, shortly after they arrived, a feud broke out among his offspring.
Lehi had four sons - Laman, Lemuel, Nephi, and Sam(uel). Laman and Lemuel were the oldest, and because they were the oldest they basically expected to have everything handed to them on a platter. They were lazy, arrogant, faithless, and cowardly. Nephi, on the other hand, was a man of both great faith and great strength; no matter what obstacle he faced, he would give his all to overcome it. Because of this, he found favor in the eyes of God as well as his parents, such that it was made clear he would be the one to succeed his father; Sam adored Nephi, and so followed his example.
Laman and Lemuel couldn't comprehend that their own misdeeds and personal failures had resulted in their being disfavored, and so instead viewed Nephi as a usurper. Their families likewise came to hate Nephi and his family, and before long the fighting between the respective families was so great that it threatened to rip the colony apart. Because of this, Laman, Lemuel, and their families were cursed with a distinctive marking so that the Nephites could tell the Lamanites apart on sight (and vice versa).
The original text noted that the Lamanites had a "dark" skin while the Nephites had a "white" skin. In the 1840s, however, Joseph Smith produced an edited and corrected Book of Mormon that aimed to fix a number of typographical errors that had been introduced by the early - and rather sloppy - printers. As part of this, he replaced these words with "impure" and "pure", respectively. (The words were, in fact, synonyms back during the 1800s - Conrad's Heart of Darkness plays with this - but their usage as such was obscure and so many people misunderstood what was going on.) The "corrected" edition was only in print for a few years before Joseph Smith's death and the flight to Utah caused the church to temporarily revert back to the original edition (the printers in England had not yet received a copy of the corrected manuscript, and so did not know to switch production to the newer version), but over the next 100+ years Joseph's revisions were re-incorporated into the text as his working papers could be located.
Much of the Book of Mormon is based on the interactions between the Nephites and the Lamanites. Yes, the Lamanites did indeed wage war against the Nephites on numerous occasions. But the Book of Mormon also recounts many instances involving righteous Lamanites. In particular, it was Samuel The Lamanite who was given the divine mission of prophesying unto the Nephites concerning Christ's birth; the Nephites were the more wicked of the two groups at this time, and so it took Samuel witnessing from atop the city's walls to shake them up.
Eventually, the Nephites and the Lamanites both became so wicked that their societies devolved into a constant state of warfare. Although the Nephites had better equipment, it availed them nothing because they had hardened their hearts against God and so had lost his protection; they were no match for the battle-hardened Lamanites, who by then had become a warrior culture akin to the Spartans.
The belief is that in time, the Lamanites eventually blended into the various Native American peoples. Because of this belief, the early church members saw the Native Americans not as "savages" like so many other Europeans did but as estranged cousins who they hoped to reconnect with. The church was so famously charitable when it came to ministering to the Native Americans on the Midwestern reservations that the Indian Agents actually kicked them out because they were embarrassed by how badly the church was upstaging them. Even non-members like explorer Solomon Carvalho (sp?) noted the lengths to which church leader Brigham Young went to negotiate with the various Native American bands that lived in and around Utah. Because the members of the church were more than eager to trade for and bargain with the Native bands (as opposed to simply taking things and brushing everyone aside), the friendlier bands quickly came to distinguish Mormons from other settlers.
So although critics of the church have frequently charged that we've been "racist" towards Native Americans, history shows that the church's behavior was the exact opposite thereof.
