The tenth century saw the continuation of Christian missionary activity into new areas.
Greek East and Latin West; The Church AD 681-1071, Andrew Louth
In the West, this activity was found in Bohemia, Poland, and Hungary (where the East also had a role), as well as in Scandinavia. In the East, there was Russia, and also in the Christian lands recovered from the Muslims. In all cases, the sources for much of our knowledge are hagiographical.
Scandinavia
In the year 1000, the Althing of Iceland (the national legislature) would embrace Christianity. As we have the story, this was influenced by pressure from the Norwegian King Olaf who, in the meantime, was holding Icelanders hostage while the matter was being decided.
It appears the focus was more on political unity than Christianization as the actual Christianization lay in the future – as did, by the way, the actual Christianization of Norway! As seen elsewhere, adopting Christianity, even if superficially, was a way by which the rulers of these lands could join into the polite society of Christendom.
How did Christianity actually spread into these lands? Evidence is scanty and subject to conjecture. Certainly the Vikings were exposed to Christianity, what with raiding monasteries and the like. These Vikings would settle in England, Ireland, Normandy – all Christian lands. They would maintain links with their Scandinavian homeland, and some Christian knowledge and practice likely passed over.
Within fifty years of the Icelandic “conversion” in 1000, an Icelander went to Bremen to seek consecration as a bishop for Iceland. Ísleifr was the son of a chieftain, and received a Christian education in a monastery in Saxony. Even before this, there were churches built without any formal hierarchy of clergy.
Perhaps this is the best conclusion I can offer.