For many reasons; some of them are:
By boat
Early North American history was affected by the fact that the North American continent was far away enough from Europe and Asia that it was unknown yet the land bridge over the Bering Strait allowed for early peoples to migrate to the region. The climate was temperate enough in many areas that animals and crops were plentiful as well.
There was really no reason people came to Americas because Christorpher Columbus thought that America was Asia. He though that because he didn't know that there was land that blocked Asia. His goal was to reach Asia because there were stories that said that there was gold in Asia so Christopher Columbus wanted that gold.
because the climate went warmer
They Used A land Bridge
cause no diseases existed
they went by animals throught the bearing straight and so
There is a theory that the North American Indians (so-called "Native Americans") crossed over from Asia by way of a land bridge that once existed in pre-historic times between the two continents - roughly along the lines of the Aleutian Island chain.
Most likely it would've either been in search of food or a home.
First to the Middle East (technically speaking, Asia) and then on to Europe
migrated by land from northeastern Asia. Henretta, pg. 7.
Neanderthals did not migrate across the Bering land bridge as they primarily inhabited Europe and parts of western Asia. The land bridge was used by early human populations to migrate from Asia to the Americas.
Birds that migrate generally do so on a North-South axis. Many birds that live on the Asian continent migrate throughout Asia. It would be unlikely, or "accidental," for birds from, for example, North America, to migrate to Asia.