Gradually, because they were trading with the Vikings and the Vikings were also working as mercenary soldiers for the Byzantine Empire, and as a counter-weight to the threat of Poland, the new country of Russia got to be more and more friendly with the Byzantine Empire. Naturally the Byzantine emperors (and the Poles too) wanted the Russians to become Christians. Around the year 1000, the Russians did become Christians, and began to build churches like those in Constantinople.
A Russian annunciation scene
Boleslaw died in 1027, and the Prince of Kiev, Jaroslaw, took advantage of the transition to Boleslaw's son Mieszko II to push Poland out of Ukraine in a big battle in 1031 AD. By 1067 AD, the Russians even moved their capital from Novgorod to Kiev. Russia was the biggest country in Europe, and the Russian people began to get rich, trading Silk Road things the Holy Roman Empire and the Byzantine Empire and the Islamic caliphate and Central Asia. Russian traders sold their own furs and amber on the Silk Road, and they bought steel swords, sugar, and knotted carpets. But they made money as middlemen, buying Silk Road steel from Iran on the borders of the Caspian Sea, and reselling it to Vikings who carried the steel north-west to Europe to make swords.
Learn by doing: go to a Russian Orthodox church service
More medieval Russian history
Earlier Russian history
More on Russian history