The dominant theory, and the one subscribed to by most archaeologists, is that Asian peoples crossed into North America across Beringia, a "land bridge" where the Bering Strait is today. In doing so, they were following herds of megafauna that were making the same trip back and forth from Asia to North America. From 12-15,000 years ago, these peoples began to migrate deeper into the continent, still following the herds of large animals on which they depended. It is believed that at least three different waves of people came across this land "bridge" (in reality a flat prairie hundreds of miles wide) over thousands of years. Eventually, they settled throughout North and South America. Evidence for this theory includes archaeological finds and genetic similarities between peoples in Asia and American Indians.
Another theory, more controversial, but not without its supporters, is that there were already other groups in North America by the time the mass migration across Beringia occurred. Evidence for the existence of these "Paleoamericans" includes skeletons found in South America and in North America, some with different skull types than those typical of the Beringia migrants. It is known, however, that the first discernible Indian culture, known as the "Clovis" culture, had spread throughout much of North and South America by around 11,000 years ago. By around 2500 B.C.E. many North, Central, and South American Indians had developed agriculture and were beginning to live in settled, stratified societies.