How did Europe become Christian?
Christians gained control of the Roman military machine, and used the power to forcibly convert everyone under Roman rule. Thus basically all the territories occupied by Rome were christianized through violence.
Back in those times, it was basically assumed that when the King converted his religion, the entire population converted with him. In other words, there was no "freedom of religion". Thus, when the Anglo-Saxon king in England was successfully converted to Christianity (after marrying a Christian woman), all of his subjects converted as well. There were a series of battles of minor kings who objected to this, but they eventually lost and thus England became Christian.
The Frankish empire was left in the wake of the collapsed Roman empire. They launched a series of military campaigns into the heart of Europe, into Germany, and forcibly Christianized all the people they came across. Charlamagne was the Frankish king who did this, and he published an edict that all Saxons who didn't convert would be killed.
Sweden was converted in a similar way as England. Basically through economic bribery, they got the king to convert, and thus the entire population was forcibly converted along with him. Converting the rest of Scandinavia was done through violence, they literally called a crusade on them and went around butchering people and forcibly baptising them.
Russia decided their religion by committee. They wanted to determine which religion would suit them best, so they accepted envoys from judaism, christianity, and muslims. Eventually deciding that christianity was the best to use, and thus the entire population was forcibly converted.>https://en.wikipedia.org/wiki/Christianization_of_Kievan_Rus%27#Vladimir's_baptism_of_Kiev
That's basically how it happened.