The system to solve a Rubik's cube uses a simple face rotation schema. You will find that the whole face will rotate either clockwise or anti-clockwise. Below is an example of all the face rotations you might need to make:
Create a daisy shape using the yellow-side of the cube.
Turn the sides around so that the edges match the centre pieces.
Match the white corners with the edge and centre pieces.
Move the pieces into their correct positions by using a right and left algorithm.
Do the following to reach the yellow cross:
Use the following algorithm to swap two wrong yellow edges.
Look for a yellow corner which is on the right position, then hold the cube in your hands with this one in the front-right-top and execute the algorithm below.
If the pieces didn't get where they belong do the algorithm one more time.
Sometimes you can't find a piece in the correct spot. In this case utilize the same algorithm for any random corner to bring one to the correct position.
Hold the cube in your hand so the upper piece you want to orient is on the FRT corner, then do this algorithm twice or four times.
Warning: DO NOT skip the last D turn as soon as you see the yellow sticker facing up at the top. Keep going until the whole algorithm is done.