The F2L (First 2 Layers) are likely the most difficult phase to master properly. Unlike the LL (Last Layer), where the algorithms are pretty much determined and "all you need to do" is to quickly recognize a fixed set of positions and memorize the algorithms, the F2L can be done in many different ways depending on which corner-edge pair you spot first. The F2L require more experience, insight, and ability to "see" the cubies on all sides, but the number of algorithms you need to memorize is minimal. The LL requires the opposite - a lot of memorizing and speed. It seems to be the case that mastering the LL is actually simpler and faster than the F2L. Many cubists report being slowed down by the F2L rather than the LL. Because I receive a number of requests for additional tips and hints on the F2L from frustrated cubers, I decided to provide another set of tips specifically focused towards the F2L.
First of all, do not sweat the cross. If you can do 3 edges and cannot figure out all 4, do just three and then, as you are inserting them, look for the fourth one. It is OK to use, say 10 moves, to do the cross instead of the optimal 7 or less. Do not try to memorize the cross at all price. Sometimes I am, too, forced to plan only three cubies if they are scattered in unfavorable positions, but I can still finish in teens.
F2L require a lot of experience but are lighting fast once mastered. Instead of memorizing the algorithms from my page, try to develop your own algs and then learn only those that you are having problems with. Do not just apply the algorithms from my F2L page blindly. Here is my advice:
You rarely, very rarely, need to remove an incorrectly positioned corner (or an edge) from the F2L in order to proceed. That will hold you back. Usually, you can do something like I described, which is fast, filled with two-side moves, finger shortcuts, and it is easy to see.
In the beginning, it may happen to you that you will be making unnecessarily many preparational turns to get the cubies into positions that correspond to the pictures from my F2L set of algorithms. If this happens, reread this article and go through the examples. There is a big space for improvization and improvement in the F2L. This is good because it means that one can develop individual approaches or discover new strategies, but it is also bad because the F2L phase is hard to explain in simple terms. To give you a better idea of how I approach the F2L and how I think out loud during solving, I prepared some examples of solving the F2L. Ron van Bruchem also gives a few examples taken from a video of his actual speedsolving.