For starters because they settled in Greenland and lived there for about 400 years. Greenland is in North America, and isn't actually farther from the mainland than Hispaniola (where Columbus landed) is. To some extent (which isn't really known) they interacted with the Dorset and later Thule cultures of Inuits in Greenland as well.

So they lived in North America and met native Americans but for some reason these questions tend to be framed to mean 'America minus Greenland', in which case there are good, more elaborate answers in the FAQ for how we know that Norse people went there around the year 1000.

The short of it, is you have written accounts from the 11th century, and the more detailed but less-credible two Vinland Sagas recorded in the 13th. The credibility for these sources is debatable (and is still debated) but what really sealed the deal was the finds at L'Anse-aux-Meadows in the 1960s at the tip of Newfoundland. (some further finds have also been made in Baffin Island since)