Until 1968 nearly all Blacks that could vote voted for Republicans. Every governor, every sheriff with a water hose, evrey state trooper that kept blacks from registering to vote in the south was a DEMOCRAT. Blacks voted for the party of Lincoln. The Democrats were the party of segregated south. It was only in the north outside inner cities that Blacks could vote. LBJ made Blacks into Demorats in less than 5 years.
How Blacks voted varied from place to place and when. Blacks were voting, of course, overwhelmingly GOP from the time of their mass-enfranchisement in the 1870s until the 1930s. In the north after the ascent of FDR, they switched over en masse, though still kept enough a foot over on the GOP side of things (although in places like NYC, Blacks were voting heavily Dem in the '40s on par with today -- a special election for a US Senate seat there in which interim GOP Senator and future Sec of State John Foster Dulles ran in, he received practically no Black votes and lost the election to a Dem). Even down here in the South (where Blacks were and remained far more Republican into the '60s), places like Memphis had Blacks voting heavily Dem pre-'60s (but that was at the behest of political bosses like Ed Crump who "allowed" them to vote as long as they did for whom he directed them to vote for). More Rural Blacks here in TN in the '60 election (those brave enough to vote) helped push Nixon to victory in this state that year. The process of conversion overall took place largely between 1932-68, not just in the '60s. It's a far more complex subject, though, then just addressing it in basic generalities.