All we know about him was recorded in Iceland in the 13th and 14th centuries, more than 2 centuries after his alleged lifetime. His deeds are featured mainly in two sagas of Icelanders, namely the saga of Greenlanders (abbreviated as GS below) and the Saga of Erik the Red (abbreviated as EsR below), called as Vinland Sagas together, in addition to the Book of Settlements, a collection of the tradition on settlers in Iceland as well as in Greenland.

Then, I'll give a very brief summary on the background of Leif, illustrated in two Vinland sagas. Narratives of two sagas sometimes don't match closely, but many people think the accounts complement each other.

In short, almost nothing to be noted or certain about him, I afraid, and I cannot say we can take any of these accounts at face value:

• Leif was a son of Eirik the Red (both GS and EsR agree) who took initiative in the Norse colonization of Greenland in the middle of the 980s. Erik the Red was also mentioned in the Book of the Icelanders (before 1133), the oldest extant historical writing in medieval Iceland, so I'd say at least Eirik was one of the most likely historical figures in late 10th century Iceland. As for Leif himself, I'd be reluctant to say anything for certain, however. While his father, Eirik was originally born in Norway and came to Iceland at first, Leif was reported to be born in Iceland while his father still stayed there before they departed for Greenland.
• Eirik was reportedly the most influential figure in 'Eastern' Norse settlements in Greenland (though both Eastern and Western Norse settlements were in fact located in the western coast).
• Leif has at least one more elder brother (EsR), or even two (GS). At least one of his brother(s) was regarded as more promising than famous Leif.
• He was converted to Christianity the court of King Olaf Tryggvason of Norway (d. 999/1000). The king instructed Leif also to convert his community of people in Norse Greenland, and it was on Leif's way to Greenland with this mission that he went astray in the ocean so that he find the new land (EsR).
• After the discovery of the new land (Vinland), he finally arrived in Greenland and many people there accepted Christianity, possibly except for his father, Eirik (EsR). So, at least he also seemed to play a certain role in the Christianization in North Atlantic, if we can trust the accounts of EsR and accept the historicity of the episode itself as well as of Leif.
• The Book of Settlements states that Leif succeeded Eirik in his farmstead, i.e. the probably most important farmstead in Norse Greenland, Brattahlíð (near Narsarsuaq) (Herman Pálsson & Paul Edwards trans. 1972: 50), probably after the demise(s) of his brother(s) as well as his rather Eirik, narrated in Vinland sagas.

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It is worth noting, however, that the mysterious island called Vinland (or Vínland) was certainly found in the 11th century North Atlantic, regardless of the historicity of Leif himself as well as the sagas, summarized above.

• The Book of the Icelanders, the oldest historical writing in Iceland (written before 1133), also mentions the name of Vinland in where Skraelingar resided (Grønlie trans. 2006: 7).
• The oldest account of Vinland is not even written in Scandinavia. In 1070s, about 2 generations after the alleged discovery of Vinland, a German clergy, Adam of Bremen, mentions Vinland as one of the supernatural islands found in the Northern Ocean, in his work. Adam claims that his informant was King Svein Estridsen of the Danes (d. 1076), and Adam does not mention Leif in his book at all.

References:

• Grønlie, Sian (trans.). Íslendingabók, Kristni saga. London: Viking Society for Northern Research, 2006.
• Herman Pálsson & Paul Edwards (trans). The Book of Settlements. Winnipeg: U of Minnesota Pr., 1972.
• The Sagas of Icelanders: A Selection, with a Preface by Jane Smiley. Harmondsworth: Penguin, 2000.