Question

How do scientists believe people crossed from Asia to North America

Answer 1

Water levels thousands of years ago used to be hundreds of feet lower, and land connecting the two continents (which is deep under water for us now) then gave people the ability to walk over it.

Answer 2

There's some disagreement on exactly how and when, but "through Alaska" is a pretty good consensus. 
There's a location in the Bering Strait where Asia and North America are only separated by about 60 miles, with a pair of islands in the middle allowing that to be broken into two journeys of about 30 miles each. There are two main theories, and many scientists believe both. One is that the first people came to North America across the Bering Strait from Siberia to present day Alaska in bands of hunters searching for food (c. 1050 B.C.) The other theory is that people came by boat from the Asian continent, going down the Western coast of North America.