That is very cool. I've never solved a Rubik's Cube (though I've never tried particularly hard) and this is making me feel stupid.
Approach it very methodically. Learn the algos. Practise. And that's really all. Here're two videos to get started: http://www.youtube.com/watch?v=mvhKNXHQqyM - http://www.youtube.com/watch?v=MaltgJGz-dU
Give yourself about 20 hours to learn and play around, by then you'll have gotten the hang of it and will probably be able to solve most arrangements with ease.
Then, experiment with commutators on the cube to look for ones that have very localized effects. Those are those 'algos' others want you to learn from a book. For example, check the simplest commutator LTL'T' and figure out how to use that as part of a larger commutator that permutes the three corners of a cube.
Yes, it will probably take more than those 20 hours (that can be done faster, I think. You need at most 4 tricks (permute three corners, permute three edges, flip two corners, flip two edges should do), each maybe ten turns to solve any cube), but it will be more fun.
It took me way more than 20 hours to solve my first cube, but the first two times I did it, I didn't even know how to solve it yet.
I've heard mine is not the normal algorithm people are taught. The one I use is totally suboptimal - but that's a wonderful thing. There's forever more to discover. It's actually a brilliant problem for the types of people that haunt HN. I implore those of you who have never tried to give it a shot. And remember, if you look online, you're only cheating yourself.
A few years ago I was determined to learn for some odd reason. From watching videos like those linked, I took a week of 2-3 hours after work to be able to reliably solve a cube using one popular simple method.
Now I seem to be able to get close, but can't remember the last couple of steps. Meh.
The accompanying Ruby Gem is pretty useful for learning the two-cycle solution (only requires memorizing 4 algorithms)
http://www.wikihow.com/Solve-a-Rubik%27s-Cube-%28Easy-Move-N...