Fridrich (CFOP) Method
First 2 Layers (F2L)
F2L (First 2 Layers) is a way of continuing after solving the cross. In this step, a first-layer corner (henceforth referred to as "the corner") and the middle-layer edge above it ("the edge") are inserted at the same time into their designated locations ("the slot"). F2L combines steps 2 and 3 of my beginner solution, but it requires approximately the same number of moves as step 3 alone. When done at full speed, F2L can be completed in less than 10 seconds!
Most F2L cases consist of two parts. One - the pairing of the corner and edge (aka "F2L pair") - and two - the insertion of the F2L pair. The moves are based solely on intuition, so algorithms are not required. However, many other sites do have so-called "algorithms" for this step. In most cases those algorithms are simply the intuitive pair-and-insert procedure optimized with moves such as x, y, d, etc. Don't start by learning those algorithms. Learn the intuitive steps first and fully understand how the moves work. It will greatly reduce the amount of memorization needed. After you get all 42 cases down (1 solved pair, 19 cases + their mirrors, and 3 symmetrical cases), then you can learn the "algorithms" if you want.
Note: In the diagrams of the cases (made with Lars Vandenbergh's amazing ImageCube script), only three sides can be shown, so sometimes, stickers from the edge cubie will be hidden from view. The red-blue F2L pair is used in all of these diagrams so the sticker that is hidden would be either red or blue, depending on which sticker is shown. For example, if the edge only shows a blue sticker, the unseen sticker would be red.
Another Note: I have not had time to make sure all these moves are correct. If you spot an error, please contact me.
The F2L Cases
In these cases, it is assumed that the corner and edge are either in their respective locations or in the top layer. If one or both pieces are stuck in another slot, you can simply move them out by inserting random pieces from the top layer into that slot. Or you can check the advanced F2L section.
For each case, there will be a "method" (how to convert it to one of the basic cases) and an "algorithm" in with a bullet in front of it. Ignore the algorithm if you are just learning F2L.
THIS SECTION IS UNDER CONSTRUCTION
These miscellaneous techniques can help you improve your speed in the step. They are for after you get the basics down so don't read these until after you do. Otherwise, they will only confuse you!