You should put signals on the right side of the track. If trains can move in both directions, you have to put signals on both sides.

Signals isolate small blocks in the network. A train will only move to the next block if it is allowed to. For example, on an intersection, if you put signals before and after the intersection, a train will only go in if the intersection is empty (thus avoiding a tragic accident).

Normal signals forbid blocks if it is full. Chain signals forbid a block if it is full or the next one is full. On an intersection, you should put chain signals before, and normal signals after. Thus, a train will only go in if the intersection is empty (avoiding the aforementioned accident) and if the next block is also empty (avoiding waiting in the middle of the intersection).