Rubik's Cube

I'm learning to solve it. Almost there, just another couple of sequences to memorise. I've been using the instructions that came with the cube (which belongs to my sister), so I haven't exactly figured out how to solve it from scratch like my mum did when she was still in school. She explained the principle of how she worked it out, but I can't quite get my head around it.

We have a Rubik's Revenge cube as well - four squares by four squares on each side. My mum's still to figure that one out.