There is a problem of terminology as the above heading indicates. The Politically Correct name is Native Americans but that does not distinguish between the at-least-two groups which would usually be called American Indians and Eskimos. The Native American terminology also means that the peoples who migrated from Asia would have to be called by an entirely different name from their descendants in America. It is just not a sensible was to designate a people. Indians, on the other hand, is an embarassingly foolish bit of terminology which perpetuates five hundred years of mistaken and uncorrected identification of the natives of America with the inhabitants of India. Anthropologists seem to prefer the term Amerindian and it is probably the best available. Eskimo, the once universally accepted term for the natives of the Arctic North America is in disfavor because it originally had a derogatory connotation. The preferred term now is Inuit which refers to the Aleutian Islanders as well as the Arctic natives.
The Amerindians identify tribally rather than racially so there is no term for their collective identity from the cultures themselves. In fact, they may not all be of the same origin. The linguist Joseph Greenberg has argued that there was another migration from Asia after the migration of the Amerindians and before the migration of the Inuits. This migration brought the ancestors of the Athabaskan Indian who occupy area in Alaska and northwest Canada. Some of these peoples migrated south in historical time (c. 1700) to settle in what is now southwestern U.S. and northwestern Mexico and are now known as the Apaches and the Navajos. For the Athabaskan people there is a term of self-identification, Na Dene, which just means The People.
The experiences of the various groups of natives in North America after European contact varied widely but the following give selection of those experiences. The point made in narratives is that the various tribes came into their occupation of the lands where they were at the time of European contact by conquest. The European conquest of the lands of North America was just the latest in a long line of conquest. No people had any claim to the land except by conquest. The archeological evidence evidence from pre-Clovis people remains is that the original immigrants to North America from Asia were exterminated by the ancestors of the native peoples found in North America at the time of European contact.