Disputed. The safest theory is they crossed the Bering Strait on foot when it was dry. It looks like this actually happened a few times. However, there are some really old artifacts in South America that question that timeline, because it would mean people had to cross from Asia and then get to South America really fast.

There's also a theory that they used small boats to travel along the shore from Asia, along the Bering Strait when it was not fully flooded, and down the western coast of America.

The book 1491 does a good job of covering the different theories.

Based on Genetic evidence, current running theory is they split from the people of Eastern Siberia about 30,000 years ago.

Most accepted theory right now is they crossed Beringia, a stretch of land that was exposed when the sea levels were much lower during the last glacial maximum. They then, were isolated in Beringia & Alaska for a few thousand years, before they made it past the ice sheets down to the rest of the Americas.

The exact method & route of getting past the ice sheets is up to a bit of debate. Old theory was a route through Canada down to the Midwest that opened about 13,000 years ago. but sites like Monte Verde, Page Ladson, Cooper's Ferry, and many more have been found that pre date the opening of that path.

So a different route has been hypothesized. The Coastal Migration hypothesis is that about 18,000 years ago, the Cordilleran ice sheet receded a bit exposing a chain of islands along the west coast of Canada. Using boats, or rafts, the people expanded down the coast, island hopping, following the Kelp highway.

But this Kelp highway theory has recently come under question as well. Footprints found at White Sands have been dated to around 22,000 years ago. Too early for the coastal route to have been viable. the dating of these foot prints is still in question. But if accurate, a new theory will have to be worked out on how people got from Beringia to the rest of the Americas.

One theory suggests that during the Ice Age (where everything on Earth was frozen–even the oceans) was the time when some of the hunter gatherer or nomadic tribes from Serbia (now in Russia) crossed the Bering Strait (A strait between the eastern end of Russia and the Western part of Alaska, today)

{Strait:- A narrow passage of water connecting two seas.} (https://en.m.wikipedia.org/wiki/File:Relief_map_of_USA_Alaska.png).

They crossed this strait unknowingly in search of food, as this is what the tribes whould do every now and then in order to survive at that time. They would relocate time to time setting camp from one place to another hunting and gathering food for their survival, hence nomadic (as farming was not known at that time hence the main source of food for the humans were other animals–more specifically meat. Even if farming was known at that time, it would have been really difficult to grow anything given the situation).

Then when the time passed, eventually the Ice Age ended and the oceans were back to being watery/liquid as they are. The people who already crossed didn't have any way back nor did they remember any way back, plus even the boats/ships were not invented at that time to cross huge bodies of water–provided if a question arises in your mind that "why didn't they use boats".

So these people eventually ended up settled in the Americas and became native to it.

This is as simple as I could explain. But if you want deep information regarding this then you can search it on YouTube, where you can easily learn more about it with visuals.