First two layers
This is the main step of the cfop method, you solve most of the cube here.
After making the cross, the cross should go to the bottom. Now you have a better view of the rest of the pieces to solve. There is no point in looking at pieces that are already solved... You will notice that on the bottom there are 4 'slots' where a corner and an edge should go. At the F2L we solve these 4 slots with 4 'F2L pairs'. We join the corner and edge and then put it in one of these slots to solve.
This step is, like the cross, also very intuitive. On the F2L it is a bit harder to see how to do things without other parts getting destroyed again. The main idea is to move the corner and edge part so that it can be solved with moves like: RU'R' or RUR'.
Some other cubists claim that the F2L is a matter of 'learning algorithms'. I think that's not the correct way of learning how to do F2L. The point of learning it intuitive is that you get a better insight in the cube itself and therefore develop a skill. This makes that you can think up your own 'algorithms' for the F2L. Also it's a faster way to do this.
However if you are stuck at a case it is handy to have a look at one of those already set algorithms. Not to learn them, but to find out how it works. By finding out you not only learn how to solve that particulair case but also the cases that require the same type of solution!
For those algorithms, check the link on the right!
advanced tips
These tips are for when you already know how to solve the F2L using intuition and wonder how to get faster at it.
The main idea about a very fast F2L is to be able to have no delays between your 4 pairs but keep moving at a constant speed. It's for most people better to be fluent and slow than fast/snappy with much delays. The trick to be able to continue turning without delays is: look ahead!
After a while you will be able to see the next pair and literally close your eyes and solve it. Because you know how to solve it already you can use the time that your hands take to solve that pair to search for the next pair you will solve. If you turn slow and constant you will have enough time to see the next one and when you are doing the moves to solve the next pair you are spending the time to look for the next one etc.
Other important tricks are to be able to solve a lot of cases from different angles. It is slow if you have to turn the whole cube instead of doing a different set of moves. And last but not least is the almighty: 'PRACTISE!'