What are the differences between them, and in what kind of sentences should I use one rather than the other?
The main difference is in the distinction what is falling from where? Generally, things that are bound by the ground are said to 倒れる. Trees, buildings, people, poles, and so on. It also carries the sense of "to collapse". 落ちる, on the other hand, carries the broad sense of "fall" and often is not interchangeable with 倒れる. It's easier to show it with some examples. Compare the following:
1: The tree fell(collapsed). It was standing beforehand.
2: The tree fell(from a certain height). It was above the ground beforehand.
3: The person fell(or collapsed), but before that he was on the ground, maybe walking.
4: The person fell, maybe from a rooftop, or a plane.
They are different in that sense.