Not a dumb question at all! It's got its own wikipedia page and was the subject of a recent monograph, which has helped renew scholarly debate on the subject. Scholars are a bit wary of the term 'Vikings', however, which many use only to refer to sea pirates around 800-1000. I'm assuming you're more specifically interested in the Christianization of the Norse people living in Scandinavia, and I'll answer your question as such.

First off, Scandinavians had long contact with Christians through travel and probably even marriage. At least some people in the early medieval world were remarkably mobile, even if the History Channel's "The Vikings" suggests that Scandinavians had no idea that Britain even existed (which is remarkably foolish). These travelers included merchants, mercenaries, and brides who traveled back and forth between Scandinavia, the British Isles, and the distant Mediterranean.

Christians probably started coming to Scandinavia in large numbers during the 800s, at the outset of the Viking Age. Monasteries and convents were easy targets for viking raiders, and a number of monks and nuns probably got picked up and sold into slavery. Most vikings probably came from modern Norway and Denmark, but it looks like most of their plunder that entered the long-distance exchange market got funneled through the Baltic Sea. Unfortunately for us (and for them), there's really no way of knowing how many of these enslaved Christians there were, or whether they had any impact on the more permanent populations of Scandinavia.

The first missionaries from the Roman church started to arrive at about the same time. Ebbo, who was himself a former slave of the French kings and had been elevated to be bishop of Reims in NE France, first asked the pope's permission to preach in the north. He was awarded the pallium, a symbolic cloak conferring him this right, in 822, shortly after Charlemagne's death. Ebbo got involved in the political infighting among Charlemagne's successors, however, and it seems like he only made a handful of trips to preach to the Danes. This should almost certainly be seen in the context of the Carolingian monarchs' efforts to establish good relations with the Danes while they were preoccupied with their own civil wars.

Unfortunately, Ebbo supported the wrong side in these wars, and he was eventually forced to renounce his bishopric and live out his life secluded in a monastery. An upstart bishop named Ansgar claimed the right to be Ebbo's successor as apostle to the north. Ansgar was bishop of Hamburg, which had recently been plundered by the Danes, and Ansgar had fled to Bremen in NW Germany. The bishop there realized that Ansgar was trying to take over his bishopric (Ansgar was ultimately successful), but in the meantime, by assuming Ebbo's missionary project, Ansgar both secured his position in Frankish church politics and put himself in a good position to reclaim rights over Hamburg when it came back under Frankish control.

It's actually fairly doubtful whether Ansgar or Rimbert (his successor as bishop of the now joint diocese of Hamburg-Bremen) spent much time if any in Scandinavia. Biographies survive for both, and the Life of Ansgar is an especially fun adventure story. But these short books seem to be more about legitimizing the bishops of Hamburg-Bremen's claims to authority as missionary bishops without a secure diocese than about offering an accurate report of Ansgar and Rimbert's missionary work.

These lives do offer us a few tantalizing details, however, which seem plausible enough. Ansgar's Life reports Scandinavian chieftains converting to Christianity as one means of challenging their kings or aspiring rulers, and both Lives show the bishops passing through markets in Denmark and Sweden, where they encountered enslaved Christians. Their biographers claim that both bishops sold whatever they could to buy these Christians out of slavery, although the persons thus redeemed often became property of the church, living out their lives in support of the missionary bishops and their priests.

All this goes to show that during the late 800s there were probably some Christian visitors to Scandinavia and perhaps even a few Scandinavian converts. But most Scandinavians encountered Christians primarily in the role of slave, which wouldn't likely have encouraged conversion. Archaeology supports the impression that few, if any, Scandinavians practiced Christianity in any sort of way that we'd consider orthodox.

Things changed rapidly in the years around 1000. Harald Bluetooth of Denmark converted to Christianity around 960, possibly as a consequence of a military defeat. He set up a stone claiming that he had made the Danes Christian, although its fairly uncertain to what this was true. But as a result, there was some church-building, missionaries had greater access to Denmark and Norway, and there were usually some bishops now traveling in the entourage of the king. And far off in the North Atlantic, the Icelanders decided to convert under pressure from the Danish king.

Although the bishops of Hamburg-Bremen still claimed the right to preach in the north, it seems like bishops from the British Isles got a head start when Harald's descendent Cnut the Great joined Denmark, Norway, and England in what historians sometimes call the North Sea Empire. Bishops circulated the North Sea as members of their rulers' retinues, and some Norse aristocrats became bishops themselves. Its hard to interpret the significance of these events in terms of belief or practice, but certainly the institutions of the church were spreading, and the Danish kings were powerful patrons.

In particular, Cnut seems to have sponsored church building as one means of asserting his royal authority. Although this was a well established practice in England, it seems to have been completely new in some parts of Scandinavia. The town of Lund, for example, seems to have been established as a royal estate and church, which superseded an earlier settlement and pagan temple at Uppåkra. Cnut sent in English moneyers to establish a royal mint, which made the town an important center of trade and tax revenue. And the archbishop of Hamburg-Bremen sent a bishop to sit in the town. The new bishops of Lund began to build a stone church, which still survives today, bringing in masons who had worked at the cathedral of Hildesheim in central Germany.

Lund serves as an excellent example of what we know of the Christianization of Scandinavia: royally sponsored, urban centered, bishop led, and catering to a mixed population recruited from across northern Europe. Other kings and chieftains followed suit, and by 1200 there were bishops established throughout Scandinavia and across the North Atlantic. There was certainly much variety to this process, and we can't be sure how quickly Christianity permeated the countryside (and some might actually argue that it never did during the middle ages).

This is what I consider a fairly conventional understanding of the Christianization of Scandinavia, although other scholars might disagree. In particular, I've left out the role of women, about whom we know little in terms of Scandinavian Christianization but who seem to have been important figures in the pre-Christian religions of Scandinavia. Also, there's a significant amount of evidence for connections between eastern Scandinavians and the Greek church, and the vikings who settled in modern Russia eventually converted to an Orthodox version of Christianity. It's hard to know, however, just how much of this Orthodox influence actually reached up to Scandinavia.