It is believed the came across from Asia. There used to be a land bridge that connected Russia and Alaska that they walked across.
There are several viable theories of how humans arrived in the Western Hemisphere, neither is exclusive of the other. As Rooster alluded to, there were at least two periods of migration across the land bridge at the Bering Strait, which is the most widely accepted theory; as well as by sea (though a far smaller percentage) in the manner that Polynesians populated the remote islands in the Pacific. All the geneology of these migrations is supported by DNA.
The question of who colonized the Americas, and when, has long been hotly debated. Traditionally, Native Americans are believed to have descended from northeast Asia, arriving over a land bridge between Siberia and Alaska some 12,000 years ago and then migrating across North and South America