There are several ways to get rid of cockroaches, differing in their effectiveness, side effects and ease of application:

Cockroaches won't stay where they find no food. However, this is more difficult than it sounds, because it means absolute cleanliness. No bread crumbs, no unwashed dishes, no leftovers in the wastebasket. Remember, cockroaches can live for a month without food, and they might even be able to subsist on the dead skin flakes that people are shedding all the time.
Perhaps the most effective way is to move to a part of the world where cockroaches are not common; usually because it's too cold for them. Canada, northern Europe are perhaps the best options.
You can buy cans of vermin-killing gas. You put the can in your room, push a lever, and get the hell out. Stay out for a few hours and upon your return you'll find dead vermin everywhere. You have to repeat this after two weeks, because it doesn't kill the eggs which cockraoches lay. Of course, this also doesn't prevent new ones from coming, so you'll have to repeat it eventually. Also, I doubt that stuff that kills vermin is healthy for people, and wouldn't rely on it magically disappearing after usage.
Roach traps
In my opinion, the best way: cheap, effective and relatively hassle-free. Lay out the traps (two or three per room, placed behind furniture, etc.), and you'll catch the first of the greedy buggers within hours. After a few days, you'll have caught most of them. Exchange the traps every couple of weeks, and enjoy relatively roach-free rooms. The only downside is that the traps smell relatively intensively for the first day or so (but continue working afterwards) and are not exactly decorative.