The Final Layer
You're almost there. In this final step you will rearrange the pieces on the top layer to get them all in place.
This will be done in two stages. The first stage involves putting the corner pieces in the right place. The second stage involves putting the edge pieces in the right place. Then we are done.
The following algorithm will switch the front two corner pieces. You will probably need to apply this algorithm a few times to line up all the corners.
Inspect your cube:
This is a large algorithm which can be difficult to remember. It can help if you brake it down into stages and try to think of it in descriptive terms as per the comments above.
Similar to the previous stage, this stage may need to be repeated several times to get everything to line up.
This algorithm will rotate the left edge, right edge and front edge of the top layer either clockwise or anti clockwise. Here is the algorithm rotating the pieces clockwise.
Remembering this algorithm becomes easier when you see it as a pattern of flipping back and forth between U and alternating R and R' moves.
For all other states just keep repeating the algorithm and rotating the top face until you create the layout above. Here are some tips to help you achieve that:
Now you know how to solve the Rubik's cube. Congratulations. The next step is to keep practicing. It will probably take you a bit before you can solve all the layers without having to refer back to the algorithms. Keep trying to work through as much of the solution as you can without referring back to the algorithms and only do so when you get stuck.
Check out our Cheat Sheet for a quick reference with all the steps on one page.
Once you have this down, the next step, if you want to improve your speed is to combine the solving of the first and second layer into one step (steps 2 and 3 of this tutorial). This is an approach called F2L or First two Layers. With a bit of practice you can do this intuitively and it will drop your times by a considerable amount.