You'll probably have either a hollow plasterboard wall or a brick / concrete wall.

Tap the wall gently and you should be able to tell.You can't screw directly into walls. You must drill a hole and use a plastic plug.(see section on plug types)
Most drills will easily penetrate plasterboard but for brick you will need a wall drill that is suitable to drill holes in brick. Ideally it should have a hammer action function which makes the job much easier on tough walls

It is crucial you use the correct plug AND screw size AND drill size. Your packet of wall plugs should tell you all this.

Tip If you don't have a drill with a depth guide on it simply use a piece of tape wrapped round the drill bit to show how deep you need to go!

For more tips on how to drill click here
Drilling

Tip Now this one really seems to impress people!
When drilling into walls (especially brick) a lot of dust will come out and make a mess.
Fold a large post-it note in to a V-shape and stick it directly under where you're going to drill. The dust falls into the post-it. Great!!