The vikings indeed traveled from the settlements on the southern part of Greenland across the water to the American continent and down along the coats.

The Norwegian explorer Helge Ingstad was, along with his wife, the ones to discover the settlements:

From Wikipedia's entry on Ingstad:

After mapping some Norse settlements, Ingstad and his wife Anne Stine, an archaeologist, in 1960 found remnants of a Viking settlement in L'Anse aux Meadows in the Province of Newfoundland in Canada.[2] With that they were the first to prove conclusively that the Greenlandic Norsemen had found a way across the Atlantic Ocean to North America, roughly 500 years before Christopher Columbus and John Cabot. He also thought that the mysterious disappearance of the Greenland Viking settlement in the 14/15th century could be explained by their emigration to North America.

From "The Vikings: A Memorable Visit to America" by Eugene Linden:

Roughly 1,000 years ago, the story goes, a Viking trader and adventurer named Thorfinn Karlsefni set off from the west coast of Greenland with three ships and a band of Norse to explore a newly discovered land that promised fabulous riches. Following the route that had been pioneered some seven years before by Leif Eriksson, Thorfinn sailed up Greenland’s coast, traversed the Davis Strait and turned south past Baffin Island to Newfoundland—and perhaps beyond. Snorri, the son of Thorfinn and his wife, Gudrid, is thought to be the first European baby born in North America.

Edit: "Vinland mystery" depicts the search, discovery and authentication of the only known Norse settlement in North America