This question comes up occasionally, and there are a few answers about the subject. In short: They crossed the Bering Strait, which separates Siberia from Alaska, sometime around 15,000 BC. At the time, sea levels were lower, enabling passage between Asia and North America.

/u/RioAbajo's answer to What is the main evidence proving or disproving the Bering Strait Migration theory? gives a great general overview of the subject.

/u/Reestilt's answer to How come America was not "discovered" via the Bering Strait?, as well as my own answer to Why Was Asian Contact with the New World Limited Compared to Europe?, both give more information on the movement of people across the Bering Strait throughout history.