Based on Genetic evidence, current running theory is they split from the people of Eastern Siberia about 30,000 years ago.

Most accepted theory right now is they crossed Beringia, a stretch of land that was exposed when the sea levels were much lower during the last glacial maximum. They then, were isolated in Beringia & Alaska for a few thousand years, before they made it past the ice sheets down to the rest of the Americas.

The exact method & route of getting past the ice sheets is up to a bit of debate. Old theory was a route through Canada down to the Midwest that opened about 13,000 years ago. but sites like Monte Verde, Page Ladson, Cooper's Ferry, and many more have been found that pre date the opening of that path.

So a different route has been hypothesized. The Coastal Migration hypothesis is that about 18,000 years ago, the Cordilleran ice sheet receded a bit exposing a chain of islands along the west coast of Canada. Using boats, or rafts, the people expanded down the coast, island hopping, following the Kelp highway.

But this Kelp highway theory has recently come under question as well. Footprints found at White Sands have been dated to around 22,000 years ago. Too early for the coastal route to have been viable. the dating of these foot prints is still in question. But if accurate, a new theory will have to be worked out on how people got from Beringia to the rest of the Americas.