How do we know the Nordic Vikings traveled to North America before Columbus and the more commonly known explorers?

The idea that Vikings came to North America began with the popularization by Rasmus B. Anderson, a Norwegian-immigrant and professor of Scandinavian studies at University of Wisconsin Madison, of the interpretation from the Icelandic saga Eiríks saga rauða ("Saga of Erik the Red") that Erik the Red's son, Leif Eriksson, traveled West from Greenland to what would be North America. Leif's part of the story also talks about how they met skraelings (meaning "little men", this was a name also given to the Dorset or pre-Inuit people they met in Greenland and name they used for the North American Natives) whom they shared a trade relationship that became strained by the natives desire to obtain the Norse steel weapons and the Norse wanting to keep their arsenal to themselves and away from potential enemies. According the saga, the settlement ended when a native was killed when caught trying to steal some of their weaponry. The settlers decided they needed to leave before they were overwhelmed by the skraelings whom were beginning attacks on their settlement.

Now while the saga had been around for a long time, the Icelandic sagas have been scrutinized for being considered more tall tales than actual historical documents due to the fact that they were preserved in oral tradition and only written about 200-300 years after the events happened. Yet the sagas also had scatterings of truth since real people were mentioned as well as real events (such as battles) thus scholars could only really debate with no real proof either way whether Leif's time in North America from Eirik the Red's Saga was real or not.

The theory became solidified with the founding of Norse style building foundations found in L'Anse aux Meadows, Newfoundland in 1960. Although many don't believe this was the same site of the settlement from the Saga and was only a temporary landing site, the find gave credibility to the saga that was once completely ignored for being myth and rewrote our more credible understanding of history.