During the last Ice Age there's a time period the archaeologists label "the Last Glacial Maximum." It's that point during the Wisconsin Glaciation where the ice reached a maximum and then began retreating to where it is today. Because so much water was held in glacier ice, sea level was up to 200 feet lower than it is today. As the ice melted, sea level rose and anything nomadic humans left behind in their migrations along the coast were washed away long ago.
At its greatest extension, the Cordilleran and Laurentide ice sheets merged around 30,000 years ago, blocking off an ice-free corridor down the center of North America. Those glaciers then continued growing to the south until the western edge of the Cordilleran sheet reached the Pacific Ocean. There are bits and pieces of land around Prince of Wales Island and through the Alexander Archipelago that were not covered with ice. Puget Sound and the Olympia Range were glaciated but not the edge along the ocean.
Maybe 20,000 years ago the heat began to rise and North American glaciers began to retreat. Glaciation in Siberia at the time was confined to alpine valleys and mountain ranges, not spread across the lower, flatter areas like it was in North America. The change in the weather pattern caused Siberian tribes to look for better climate and, at the time, that path lead to Alaska. The heat peaked somewhere between 14,000 and 11,000 years ago, then cooling caused the glaciers to grow southward again. That change in the weather of Alaska caused those same tribes to head further south along the coast.
There is an archaeological site at Monte Verde, Chile, about 50 miles south of Santiago. Remains found there have been carbon-dated to be about 14,000 years old.
The map above offers a hypothetical scenario for the peopling of the Americas. Possible migration events are described in the overlaid text, coloured according to consensus region of origin (Beringia immigration vectors are represented in blue; Siberian immigration vectors in shades of purple).
Also shown are some key archaeological sites in North America and Siberia, and the type of evidence (genomic, mitochondrial DNA, Y-chromosome DNA and archaeological) currently supporting each hypothesized migration. Shading depicts the extent of Beringia during the Last Glacial Maximum. (kyr = thousand years ago.)
Basically, what is being indicated is that mankind came to the New World from Asia beginning somewhere between 26,000 and 18,000 years ago. They walked over from Siberia along the southern edge of the Beringia Land Bridge. That land bridge existed courtesy of the Ice Age locking up so much of the global water supply as ice.
Much of the evidence supporting the routes and dates of migration is derived from the genomic sequencing of well-preserved ancient human remains. The dates of some of these coincide with the projected timespan of the Clovis Culture, a culture primarily defined by the shapes of their arrowheads and knives. Only recently have human remains been unearthed that tied the genes to a Clovis Culture burial site. The remains were of a less than 2 year old boy and his bones were surrounded by Clovis artifacts. The body was interred between 12,707 and 12,556 years ago in central Montana. His genome sequence on the maternal side belongs to the strain of humans who advanced down the Pacific Coast beginning around 17,000 years ago and reached Monte Verde in Chile at least 14,600 years ago. Only about 1.4% of modern Native Americans have the sequence, it is more commonly seen in indigenous people in Central and South America. On the other hand, in the Y chromosome is a sequence still seen in many of today's Native Americans.
There is also speculation about a second wave of migration about 13,500 years ago from Siberia through a gap between the Cordilleran and Laurentide ice sheets. Those genes brought a sequence seen in modern Athabascans, Chipewyans and other eastern groups. They seem to have spread southward and eastward to occupy most of North America east of the Rocky Mountains. Then came the events of the Younger Dryas and many of them in the northeast part of the continent and along the Atlantic shore were wiped out almost overnight.
The Younger Dryas may have been a naturally occuring cooling event but the timing coincides with a massive comet strike across northeast North America, Greenland, Iceland and northwestern Europe. The planet cooled for about a century and the glaciers grew again for about 1,300 years. Then came a period of rapid warming and glacial melting, bringing sea level to about where it is today. During the Older and Oldest Dryas periods, the cooling and rewarming periods were much longer. The "Dryas" name comes from a genus of Arctic flowers whose preferred growth medium moved north and south with the glaciers as they expanded and contracted.
If the comet strike theory is correct (and places where pieces of it struck the ground have been identified), northeastern North America was likely almost completely depopulated. The resulting blast waves and fires would have touched most of the rest of the continent, except west of the Rocky Mountains. This would also explain the end of the Clovis culture, a set of technologies that had spread east across the continent from its beginnings in the Southwest.
Another expansion of the Bering land bridge brought the Neo-Inuit migration eastward along the shore of the Arctic Ocean, about 800 to 1,000 years ago. They eventually made it across northern Alaska, the Yukon, Northwest Territories, Canadian Arctic Islands and on to western Greenland.
Today's Puebloans carry gene sequences pointing back to the original migration from Siberia along the Pacific Coast around 15,000 years ago. The Apaches and Diné trace their lineage back to a group of Athabascans who came across the land bridge around 13,000 years ago. There are many people who carry traces of both.
Map courtesy of Nature Magazine.
PS: The above is kinda the accepted story. There are anomalies out there that point to humans being in the New World more than 20,000 years ago but, as in so many things, there is argument from the entrenched perspective and a shortage of (accepted) evidence from new perspectives.