Born of Erik the Red and Thjodhild c. 970, grandson to Erik's father Þorvaldr Ásvaldsson who'd been exiled from Norway to Iceland, Lief was raised by Tyrke--a thrall of Erik--accepted in time as a hirdman by King Olaf Tryggvason of Norway, and charged later with the mission to bring Christianity to Greenland. In the year 1000, Lief heard tell from a merchant Bjarni Herjólfsson about a land farther to the west. Buying Bjarni's boat and gathering a 35-man crew, Leif set sail to find it and landed at what most scholars believe is Baffin Island, named in the Grænlendinga saga as Helluland (Flat-Rock Land). Sailing on, he came next to what is probably Labrador (Markland, Forest Land, in the saga), and then two days beyond he reached a place he named Vinland (Wineland or Pastureland), where he and his men wintered before returning to Greenland with grapes and timber, after which Lief settled into the family estate Brattahlíð in Greenland and, to his father's displeasure, began preaching Christianity to the Greenlanders.
It is thought Vinland is modern day Newfoundland or the lands of that area including but not limited to Newfoundland.
In the 1960's, archeologists discovered a Viking settlement on the norther tip of Newfoundland, confirming that the Vikings had indeed discovered North America as the sagas told--500 years before Christopher Columbus.
(There is inconclusive but arguably growing evidence that Northern Europeans reached what today is Canada even before the Vikings did, most likely by following the southern edge of the ice sheets from Europe and across the Atlantic.)