General solutions.

Layer by Layer.

Singmaster's Layer by Layer method has always been one of the most used methods to solve the cube.

Here is a very good video of how to solve the cube. It gives you a visual way of solving the cube, he explains all moves, and all moves are visable in Singmaster notation. How to solve a Rubik's Cube

Here is a site that tells you just by figures how to solve a Rubik's Cube. The advantage is that you can practice without having to pause the video from the link above.

Wikihow:Solve a Rubik's Cube

Notice that both links above are the easiest way to solve the cube, but contains more moves than required. It is just an easy to memorize algorithm to solve any cube. If you practice this method for about two days, then you should be able to solve any cube in around 3 minutes.

Also notice that until you've mastered all algorithms, an easy to way to understand what algorithm does what is to apply the algorithm to a solved cube. This way you can see exactly what it does, like permute the top corners, or flip two edges.

Fridrich's Method.

When you've familiarized yourself with the Layer by Layer method and you want more, and especially faster, then Fridrich's Method may help you out. But beware, it is more difficult and should only be taken into concern when you've mastered the Layer by Layer method.

Fridrich's Method.