Short answers, pulled from the story.
The traditional date for the settlement of Iceland is 874, drawn from the medieval histories Íslendingabók and Landnámabók, with the wider Age of Settlement running from 874 to 930. Some archaeological evidence, including tephra dated to about 871 and sites possibly predating 870, suggests activity may have started slightly earlier than the traditional date.
Landnámabók names Naddoddr as the first Norseman to set foot in Iceland, though he stayed only briefly. Garðar Svavarsson was the first to stay through a winter, and Ingólfur Arnarson is credited as the first permanent settler, building a farmstead at Reykjavík.
Medieval Icelandic sources blame civil strife under Norwegian king Harald Fairhair, including his heavy taxation of farmers, for pushing people to leave. Modern historians instead point to a shortage of arable land in Scandinavia, the appeal of unclaimed territory, valuable resources like walrus ivory, and greater resistance to Viking raiding in the British Isles and continental Europe.
Genetic studies show about 62% of Icelanders' matrilineal ancestry traces to Scotland and Ireland, while about 75% of patrilineal ancestry traces to Scandinavia. Archaeogenetic evidence suggests the original settler population averaged 56% Norse ancestry, lower than the 70% found in the modern population, partly because many Irish and Scottish settlers arrived as slaves.
The Age of Settlement is traditionally considered to have ended in 930, when the Alþingi assembly was founded at Þingvellir and the Icelandic Commonwealth period began. Landnámabók records about 1,500 farm and place names and more than 3,500 people by that point, though archaeological evidence shows immigration continued through the tenth century.
About 40% of Iceland was forested before medieval deforestation, compared with roughly 2% today. One study attributes the deforestation mainly to clearing land for pastures and home-fields rather than to settlers' need for fuel and building material, and the Icelandic Forest Service now aims to raise forest cover to 10%.