Believe the domestication of dogs occurred along time ago during the time of hunters and gatherers. Early man saw the benefit of having this ally along on hunts to help locate or take down game. For how they arrived to the Americas, more than likely the same thing with the Bering Strait landbridge during the time before the ice age.
Early dogs probably also served to help in protection as when large groups of early man settled in a location for a bit, wolves and other predators more than likely tried to come into the camp only to have the dogs warn the humans of the approaching danger.