Basically, it started with Vladimir I, who was the Prince of Novgorod, and then of Kiev, from 980 to 1015 AD. In the beginning, he was a pagan, who had relations with many women and everything. But, and mostly for political reasons as he wished to have more international impact than what he had, he realized most major powers were monotheistic, whether it be Islam, what would later be known as catholicism and eastern orthodoxy (so Christianity from Rome and Constantinople) and even to a lesser extent Judaism.

So apparently, he sent envoys to various places to see which religion was the best, to evaluate the "pros and cons" of each religion. In the end, he chose Eastern Orthodoxy, and if you go on Wikipedia on the Vladimir I page, you'll see a nice quote about Constantinople that would have been said by his envoys, about how it was an amazing city and all.

And when you think about it, if he had chosen Islam, he wouldn't have the right to eat bacon. I guess that's another "pro" in the "pros and cons" list for Eastern Orthodoxy, at least THEY could! (Just kidding of course).

So basically, there it is. It was mostly for political reasons that Vladimir the First chose to switch to monotheism, and in the end he chose Eastern Orthodoxy. You can read more about Byzantium and the race (with Rome) to conversions in the Balkans and, in this case, Russia) in some history books about the Byzantine Empire, like the one from John Julius Norwich... It's a pretty good one, that's the one I had to use when I took a class on the Byzantine Empire during my Bachelor in history...

to tag onto this question: how valid are the claims that Vlad I may have been Muslim at the time of his conversion?