How did the slaves escape from their plantations?

They were not generally locked up or restrained in any way. Escaping from the plantation was literally as simple as walking off Into the Woods.

Escaping TO somewhere, on the other hand, was the real trick of the matter. Hunting down escaped slaves was lucrative and there were a lot of people doing it full time. Also, escapees had to travel in the dark and off the roads, so escaping could very well mean getting lost or seriously injured, and then starving to death. As time moved forward through the 1800s, the underground railroad developed and is well known to have moved a lot of slaves into the North.