This section contains enough information for you to solve your cube without much thinking. Don't look at it if you like to solve puzzles by yourself.
Here are some operations that may prove to be useful in solving the cube puzzle. The first three move the cubies as indicated, but some of them also may flip the edges or rotate the corners. The final two operations leave all the cubies in place, but flip edge cubies or rotate corner cubies as indicated.
There are almost certainly better methods available--these are just the ones I found myself. For the initial stages of solving a cube, they are also too powerful. If you're just trying to get the top face correct from a completely jumbled cube, you don't really care what you do to the other cubies, but all the examples below are very restrictive--only the indicated cubies move; the others are left fixed by the operations.
Warning: If you're starting with a pure cube, be careful to follow the instructions below exactly--one error and your cube will be trashed. Take it slowly and remember that is ``back'', not ``bottom''. Also remember that to undo an operation, you can reverse the steps starting from the back. For example, to reverse , perform . Also, be sure to keep the top cube on top and the right cube on the right as you do these operations. For example, if the top cube is white when you begin, make sure it stays white through all the operations. Another way to avoid problems when you are a beginner is always to twist the faces with your right hand. Then if it is one of , , , , , or , you will twist in the direction of your thumb. If the operation is among , , , , , or , you'll twist away from your thumb. If you're left-handed, think different.
Finally, it is much easier to study movements if you can begin with a solved cube, but it's pretty easy to make an error and to wind up with a cube that's totally jumbled. If you have no idea how to solve it, this situation can be pretty depressing. But there is a way to cheat-- just take the cube apart, and put it back together in the solved configuration. To take the cube apart, the easiest way is to take a screwdriver and to put it between the center cubie of a face and one of the edge cubies, and then to pry out the edge cubie. Once it's out, it is easy to remove all the rest of the cubies, leaving a central ``skeleton''. From the skeleton, put the cubies back one at a time into their correct positions.