Solving a Rubik's Cube?

Hello, I was just wondering how someone would go about solving a Rubik's Cube, and please don't say "Google it", I'm not looking for a internet tutorial really, I was wondering how someone could solve it with the bare basics, just the cube, a pencil, and paper, and please don't say "trial and error" either, i'm mainly just curious as to how someone would go about solving it mathematically. Any mathematicians here? ^^;