There are some strong arguments over this question. The traditional hypothesis is that ancient humans spread across Asia and, during the Ice Age when sea levels were far lower, followed the Bering Land Bridge from Siberia into Alaska, after which they would wander the west coast and possibly spread inland. Others have argued that we underestimate the sailing prowess of ancient humans, and that they might have sailed across the ocean, winding up in South America first. However, the pattern of artifacts found to date does not yet support this.
A more recent hypothesis is that humans spread up through Northern Europe, primarily sailing from island to island, including Greenland and Iceland, eventually hitting northern Canada and traveling down the east coast. There are a few artifacts to suggest this might be true, but so far, the early Clovis People fossils and artifacts still seem to support the belief in the Bering Land Bridge.