You should try the Shutter Priority mode for blurred shots. This is labelled "S" or "Tv" depending on your camera (not a Canon person, sorry).
The shutter speed you should use really depends on what you're shooting and how you're holding the camera.
If you, say, shoot cars or snowboarders, then you can use a reasonably fast shutter speed (around 1/50 or 1/30) without losing much background detail from hand-shake. If you're shooting slow objects (like a moving town centre) then you'll need to use a tripod.
If you've got a tripod, then you can get away with pretty much any shutter speed. Of course, it's very useful to use the Self Timer on your camera to completely shut out any camera shake.
If you can tell us what you're shooting, and how much blur you want to get, then I might be able to help a bit more. Good luck!