In 986, Bjarni Herjolfsson saw a strange land to the west of Greenland now believed to be Baffin Island. Because of the earth was going through a "hot period" the land seemed hospitable but Bjarni was in a hurry to get home so he and his men did not visit the land. No one took interest in Herjolfsson's claim except a recent Christian convert named Leif Erikson.
The story of Leif Erikson is told in the Vinland Sagas (the Saga of Erik the Red and the Saga of the Greenlanders). Erikson set out around 1000 and first set foot on Helluland (now day Baffin Island). There they made contact with the Skraelings or natives of the area. While there is a story of Vikings saving a pair of Indians no meaningful cultural exchanges took place. After Helluland the Vikings traveled to Markland (Labrador) had chopped down trees to take back to Greenland (Labrador is now too cold to grow the tree which was chopped down).
A settlement related to the journey of Leif Erikson is the colony at L'Anse aux Meadows. Here the Vikings hope to have a launching base for colonization of North America and trading with the natives. However, cultural misunderstandings with the natives including a Viking bull on a rampage turn the Indians against the Vikings. Rather than stay and fight it out in a strange new world the Vikings instead leave North America and return their attention to Europe. It would take an Italian in Spain's service to reopen the New World to European interests.
Today Leif Erikson's impact on America is a mere footnote. Sad but true. However, let us not forget those first Nordic-Americans who tried, but failed, to live with the natives and call America "home."