There are many ways to solve Rubik's Cube. Here are some of the simplest solutions. Not the quickest, but the easiest to learn.

3x3x3 beginners method
Beginner's giude (pdf): A really simple solution, with only a few algorithms to learn, with really clear child-friendly notation. The real advantage of learning this method is that it upgrades to speed methods very easily. (It is same as our Beginner's giude (pdf), almost)

4x4x4

5x5x5

6x6x6

3x3 Gear cube



Pyraminx

Megaminx

Skewb