I can't give the whole picture, but I can try to explain how it happened in Norway. It had a lot to do with the "modernization" into a proper medieval state.

• 793-1000: The norse traders, settlers and pirates get into contact with Christian people more and more often.

• 10th century: The oldest remains of Churches.

• 935-961; Hákon Aðalsteinsfóstri, known as "the good" is the first Christian king. Raised in England by king Aethelstan. He brings the first bishop and tries to convert people on a smaller scale, until the chiefs in Trøndelag forces him to participate in a blót, unless he wants to loose his title. He let them have their faith in peace after that, but did manage to give the religion a true presence.

• He did not rule all of Norway though, as the Danes had power in the south-east, around today's Oslo. A rune stone after the Danish king Harald Bluetooth (dead 985) says he won Denmark and Norway, and made the Danes Christian.

• Haraldr gráfeldr was the next king. 961-970? didn't matter much. "Gunhild's sons embraced Christianity in England, as told before; but when they came to rule over Norway they made no progress in spreading Christianity -- only they pulled down the temples of the idols, and cast away the sacrifices where they had it in their power, and raised great animosity by doing so."

• Hákon jarl inn ríki was the defacto king in Norway from 970 to 995. He was in theory a vassal of the Danish king, but renounced Christendom a while into his rule. He was a good commander and beat the Jomsvikings and the Germans. His end came after he had become a unfair ruler, and forced himself upon noble women. The people in Trøndelag revolted and he was killed by his thrall while hiding under a pig sty. He was the last heathen ruler.

"Hakon the earl, so good and wise,

Let all the ancient temples rise; --

Thor's temples raised with fostering hand

That had been ruined through the land.

His valiant champions, who were slain

On battle-fields across the main,

To Thor, the thunder-god, may tell

How for the gods all turns out well.

The hardy warrior now once more

Offers the sacrifice of gore;

The shield-bearer in Loke's game

Invokes once more great Odin's name.

The green earth gladly yields her store,

As she was wont in days of yore,

Since the brave breaker of the spears

The holy shrines again uprears.

The earl has conquered with strong hand

All that lies north of Viken land:

In battle storm, and iron rain

Hakon spreads wide his sword's domain."

• Óláfr Tryggvason (king 995–1000) was the king who did most of the real work to make the land Christian. As many of these kings he had converted while out travelling. Leif Eirikson, who discovered america is said to have been baptised by him. He was strict, and would burn in practitioners of magic and kill heathens unless they converted, as was standard.

The king let all these men be seated in one room, which was well adorned, and made a great feast for them, and gave them strong drink in plenty. Now when they were all very drunk, he ordered the house be set on fire, and it and all the people within it were consumed, all but Eyvind Kelda, who contrived to escape by the smoke-hole in the roof.

In the region of Trondheim he was invited into the temple to "observe" their customs, as the landowners wanted peace with the king. In there he cut the statues down, as his men outside cut down the main oponent of his, Iron Beard. Without that chief to speak for them, they did not dare oppose him and were "baptised". Similar things happened all over, as he went from assembly to assembly and forcefully converted people.

He died after a battle with the allied Swedes and Danes against him. It is worth noting that the Christian Dane allied with the Pagan Swedish king to kill the Christian Norwegian king.

• After that the Danes instated their own Christian vassals over Norway. Things calmed down a bit, but paganism was severely prosecuted still.

• Óláfr "The holy" Haraldsson is the most famous king in Norway when it comes to Christendom. He is a Orthodox and Catholic saint, with hundreds of churches dedicated to him in the Nordic countries and Russia. He was probably bapticed in Rouen, and was king from 1015-1028 when the landowners were tired of him and revolted in favour of the Danish king. He fled to Russia for 2 years before returning in 1030 to die and be declared a saint.

He continued as the king before, and during his reign Christendom had become the main region in the land. A few places still were a bit behind, but he dealt with them aggressively. When the chiefs in Trøndelag, who had "converted" earlier were busted in still sacrificing and praising the old gods, even though they had assured him they did not, he killed the main guy, Ölvir á Eggju, and burned his farm down.

"If I must say the truth, king, as it is, I must declare that in the interior of the Throndhjem land almost all the people are heathen in faith, although some of them are baptized. It is their custom to offer sacrifice in autumn for a good winter, a second at mid-winter, and a third in summer. In this the people of Eyna, Sparby, Veradal, and Skaun partake. There are twelve men who preside over these sacrifice-feasts; and in spring it is Olver who has to get the feast in order, and he is now busy transporting to Maerin everything needful for it."

After his death the Danes again had the rule for a while, but now Christendom was the undisputed religion in the land, with churches being built and people forcefully converted. And the new Christian laws ruling.

Sources: Store norske leksikon, and the medieval Sagas.