Recently, a nephew asked about how to solve a Rubik's Cube. I couldn't sit down with him to show him what I knew, so I looked around the web for explanations. I was surprised by two things: first, that all the pages offering solutions seemed to offer the same one, even down to the colors discussed: "Start by making a white cross, ..., finally, finish the yellow side."
Second, that the techniques (or "algorithms") were often given without explanation. They're presented as something to memorize.
My own solving technique uses a few algorithms constructed in a certain way that I describe in Two-Part Rubik's Algorithms. I wrote them up as a resource I hope my nephew will be able to use.
BTW, that page makes use of Conrad Rider's impressive TwistySim library.