How did the first Americans get to north America?

How indeed? For the Inuit and other cultures that in the north, they would travel by foot and boat along the interface between ice, ocean and lands. But the Inuit were almost certainly not the First Americans as they are among the most recent.

The most politically acceptable answer is to say the First Americans got here by using the Bering Land Bridge and walking from Asia. These people would be part of the Clovis culture. This theory underpins the Aboriginal claims to special racial status as it assumes North America was devoid of people.

An alternative theory called Pre-Clovis has other routes being taken. This theory is based on the many finds which predate the Clovis culture and has people arriving by boat or as the Inuit traveled, following the interface between ice and ocean. The Inuit method is most controversial as it would have Europeans being Pre-Clovis possibly reversing the special status claimed by many groups today.

Given the politics, special racial status, and huge amounts of money on the line it is not an easy scientific answer but the safest answer is walking across the Bering land bridge.