These are the different sensor sizes:
- Full frame sensor (Nikon's FX, Canon does not use special term): 36 x 24mm, no crop (actual size might differ slightly between brands and cameras)
- Canon's APS-H: 27.9 x 18.6mm, crop factor 1.3
- Canon's APS-C: 22.3 x 14.9mm, crop factor 1.6
- Nikon's DX: 23.6 x 15.8mm, crop factor 1.5 (23.1 x 15.4mm, crop factor 1.55 for Nikon 3100)
The effects of crop factor to the lenses is that the smaller sizes lessen the angle of view, but as the focal length is universally adapted to represent the field of view, you can multiply the focal lengths by the crop factor to get the indication for angle of view.
In example if you take 18-55mm zoom, it's effective angle of view on APS-C is equivalent to 18x1.6-55x1.6 ~ 28-90mm lens on a fullframe camera.
You might find this discussion about focal lengths and their equivalents useful.
When shopping for lenses, one should keep in mind that when you have camera with cropped sensor, both fullframe (Canon's EF, Nikon's lenses without DX marking) and cropped sensor (Canon's EF-S, Nikon's DX) lenses are usable on your camera, but lenses made for cameras with cropped sensor are not usable on fullframe cameras.