There are three different car classes and boost systems in Burnout Paradise:
The way you earn boost in these classes is quite different.
In a stunt car the most efficient way to earn boost is by doing stunts. This includes jumps, flat spins, barrel rolls, smashing billboards and so on. You also earn some boost by drifting, doing near misses and driving in oncoming.
In aggression class cars you earn most boost by doing takedowns, grinding, smashing and so on.
The way you use it is the same except for in Speed where you have to have a full boost bar before you can use your boost. This is often referred to as Burnout 2 type boost. When using a car with speed type boost you can also do boost chaining.