Short answers, pulled from the story.
The traditional date for the definitive Christianization of Kievan Rus' is around 988, when Prince Vladimir the Great was baptized in Chersonesus and ordered the mass baptism of Kiev's population in the Dnieper River. The exact year is disputed by historians, and the broader process had begun centuries earlier.
Vladimir's conversion was tied to a military and dynastic agreement with Byzantine Emperor Basil II. In 987, Basil sought Vladimir's military help against a rebellion led by Bardas Phokas, and Vladimir agreed on the condition that he be allowed to marry the emperor's sister Anne and that both he and his people would convert to Christianity.
Several early rulers reportedly converted before Vladimir, including Askold, Dir, and Olga of Kiev. Olga, who ruled as regent, visited Constantinople either in 945 or 957 and is associated with baptism, though the chronicle does not explicitly state where the sacrament took place. Her son Sviatoslav remained pagan and demolished churches during his reign.
Vladimir ordered the wooden statue of Perun, the supreme Slavic god, thrown into the Dnieper River. Men with staves followed the idol downstream to prevent it from coming ashore. Vladimir had erected that same statue only eight years before its destruction.
Patriarch Photius of Constantinople reported in 867 that the Rus' were converting enthusiastically and dispatched a bishop to their territory. However, his efforts had no lasting consequences, and the Primary Chronicle describes the Rus' of the 10th century as still firmly pagan. Historians debate whether Photius's mission was followed by a second, more successful mission under his successor Patriarch Ignatius.
The spread of Christianity outside Kiev met serious resistance. Novgorod was baptized only in 989 after fierce clashes, with Vladimir's uncle Dobrynya reportedly using force. Pagan uprisings continued for nearly a century, including one in Novgorod in 1071 in which Bishop Fedor's life was threatened.