There are some good detailed answers already, but I would summarize it as:
에 denotes motion towards a place, and location of things (including abstract things, like times).
집에 가다 - To go home
그림이 벽에 걸려 있다 - the picture is hanging on the wall
내일 오후에 전화할게요 - I'll call you tomorrow afternoon
에서 denotes motion from a place, and location of actions.
집에서 오다 - To come from home
도서관에서 공부하다 - To study at the library.
I'm sure there are lots of other special cases, but I think that's a useful simple way to think about it.
I don't recommend trying to equate either to the meanings of particular English prepositions, as there isn't a very tidy 'mapping' between them.