In Iceland, 1000 AD will most likely be remembered as the date of Christianization. This took place over many decades, of course, starting with missionaries in the 800s, but the Alþing (the legislature) made the decision to have Iceland be a Christian state in 999 or 1000.
Would the average islander have been Christian in 1000? Historian Orri Vésteinsson suggests tells the account of a priest, Þormóðr, who was the sole priest on the island in 1000 and was tasked with baptizing the whole population. Vésteinsson says "it must have taken a long time to establish any basic Christian practices," which speaks not only to the prevalence of Christianity (likely low), but also the sparse nature of settlement. He goes on to say that there are only five churches on the island recorded as being built before 1100, missionary bishops not arriving until 1020, and so on. Vésteinsson caveats all of this information by saying the empirics are few and far between to give us a clear picture. He's making the best with what he has at his disposal, as is so frequent in cases like this where the record is thin and the supporting material is practically nonexistent.
Even though our knowledge of the religious state of the country may be shaky at best, it may be the part of millennial Icelandic life we know the best. The Íslendingabók, a national history written in the 12th century, tells of major milestones in the country's history. Christianization is part of this, but the daily life of people 100+ years prior to the writing of the book, which itself is a rather slim volume, doesn't make the cut.
So what was life like in Iceland around 1000 AD? The country was in the process of Christianization, which was about to be accelerated by decree of the legislature. Daily life, however, we don't know much about (or at least I can't remember reading other sources that have spoken about it).
Sources:
Karlsson, Gunnar. The History of Iceland. Minneapolis, MN: University of Minnesota Press, 2000.
Vésteinsson, Orri. The Christianization of Iceland: Priests, Power, and Social Change, 1000-1300. Oxford: Oxford University Press, 2000.
If you're interested, you can also check out a (maybe not quite perfectly) translated version of the Íslendingabók here: https://en.wikisource.org/wiki/%C3%8Dslendingab%C3%B3k