Learning the Cube
Before you build up speed, make sure that you are fully acquainted with your Rubik's cube. This can be done by knowing the sequence of colors and understanding the way the pieces move. For example, the center pieces of each side never move, meaning white is always opposite yellow.
Layers
The typical method for solving a Rubik's cube is through layers. This is done by picking a "top" side, and then systematically solving downward. You might solve the edges of the top, then the corners, then the middle corners, and finally the bottom.
Expanding
The other method speedcubers often use is starting at one corner and building the cube from there. This is done by positioning and orientating a two-by-two cube in the corner, and then completing the final edge of the cube.