There is solid evidence that the Vikings attempted to found a settlement in the region they called "Vinland". Archaeologists in 1960 found remnants of a Viking settlement in what is today L'Anse aux Meadows in the extreme north of the island of Newfoundland, here's a photo of the site and a reconstruction of one of the buildings, as well as a model reconstruction of the settlement.

As for how the settlement failed; no one knows for certain, but reasonable outcomes include the failure of the Vikings to keep the settlement resupplied with provisions, hostile contact with native Inuits, or just eventual abandonment.

If you're interested in reading further into the excavation site, here's a good read for you:

Ingstad, Helge; Ingstad, Anne Stine. The Viking Discovery of America: The Excavation of a Norse Settlement in L'Anse Aux Meadows, Newfoundland. Breakwater Books. (2000)