I can only speak for eastern block. First issue is that you can't really cross borders without special permission given by government. This permission wasn't easily gained either. Officials feared that if you once leave , you will never come back , so even if you somehow managed to get it , there were more restriction like you had to leave your kids home or something similar. This didn't stop many people from doing it. In Czechoslovakia there were two big migration besides the usual when border officials didn't cared and let everyone out who wanted to leave . First was in 48 after February revolution and second in 69 after Prague Spring . Otherwise it dependent reallY heavily on your connection , if your parents/you was/were in party and so on. Artists and sportsmen could leave but they usually returned because of their families but couple stayed like Peter Stastny (hockey player) .For ordinary people leaving was almost impossible and if you had record of bad behavior or was known for opposing party ,your best bet was to swim through Donau or jump the fence but most likely you would get shot doing it.Basically it was really hard to leave and even if you could there were still some though restrictions. Usual path was through Jugoslavia to Italy or East Germany to Denmark or West Germany.