The main problem with the Scandinavian attempts to colonize continental North America is that they were never serious about it; there were never more than a one or two hundred Scandinavians in North America, excluding Greenland of course. You don't take a continent with a two hundred people.
In 986 CE, a Scandinavian merchant named Bjarni Herjólfsson sailed from Norway towards Iceland to visit his father, who had a farm there. Arriving in Iceland, he found out that his father had left for Greenland with Erik the Red; as a consequence, Bjarni Herjólfsson left from Iceland towards Greenland.
En route from Iceland to Greenland, Bjarni's ship was blown off course by a storm and arrived on the shores of a lush verdant land well west of Greenland. After repairing his ship, he sailed north, and spent some time looking for Greenland, for neither he nor any of his crew had ever been there. Eventually they found Herjolfsnes, a Scandinavian settlement in Greenland, and Bjarni was reunited with his father.
Word spread about the land seen by Bjarni, the Greenlanders being most interested in the reported abundance of timber. Leif Erikson, the son of Erik the Red, armed an expedition to go look for Bjarni's land; this would have been around 988 CE.
Point of departure: The expedition really ought to have been led by Erik the Red himself, not by his son Leif. In real history, Erik suffered a riding accident, so that he was unable to go exploring. Had the expedition included Erik the Red, with his strong personal authority, the attempt to move west would have been treated more seriously.
Leif and his men overwintered in a fertile and green country, full of vines and grapes, which they called Vinland. It is possible that the archaeological discoveries at L'Anse aux Meadows in Newfoundland may be the remains of Leif's camp, Leifsbúðir. When spring came, Leif and his men left and returned to Greenland with a cargo of grapes.
Point of departure: The expedition, instead of one ship and 35 men, has three ships and 100 men, brought from Iceland and Norway in addition to Greenland. Instead of visiting over winter and leaving, two ships and 70 men remain in Vinland and fortify the camp, and one ship is sent back to Greenland, Iceland, and Norway to drum up colonists desirous of settling in a new, green, fertile land.
In real history, Leif never returned to America. Instead, his brother Thorwald came for a visit in 1004 CE. He promptly initiated a deadly conflict with the natives, as if he wanted the colonization efforts to fail. He was followed by Thorfinn Karlsefni who led the only real attempt by Norsemen to colonize the New World.
Point of departure: instead of a pitiful and half-hearted attempt with two hundred people, the Norse come with a thousand people in 20 ships, mostly from Norway and Iceland. Their settlement holds off the natives, and thrives...
If one man had not fallen off his horse, if the Norsemen would have shown a minimum of diplomacy, and if the colonization attempt had been just a little more serious, a Norse empire in the west could have arisen to rival their success in the east, where the Rurikids created what would later be the Russian Empire.
Hat tip to Mark Olson for finding the perfect motivation factor for a sustained attempt at colonization: the Norse settlers in Newfoundland find the Grand Banks; a fishing a fish-processing industry emerges, anchoring the colonists in the newly found land.