The origin of using "how" as a greeting is "one of those rare bits of frontier rubbish that actually has some basis in fact. There is no such thing as a universal Indian greeting — the original inhabitants of North America spoke some 500 different languages — but we do find variants of "how" in the native speech of many Plains Indians tribes, who spoke versions of a major language called Siouan. The Tetons said "howo" and "ho," the Dakota had "hao" and "ho," and the Omaha had "hau" (and maybe "ho" too, but I didn't find it in my Omaha dictionary.)
The precise meaning of these words varies with the ethnographer who recorded them, but from my reading of various ancient Native American tales (rendered in the original, of course) I deduce that they served as a sort of all-purpose introductory adverb or interjection along the lines of "well," "hey," "so," or "now," as in, "Now see here, white-eyes …" You can imagine how ignorant pioneers who heard this at the beginning of every Indian soliloquy might come to regard it as a greeting. At any rate, the word eventually found its way into the public consciousness."