First off you should know that, in my opinion, the edges step is the most important step in transforming a scrambled 4x4x4 into a scrambled 3x3x3. This step takes the most time when compared to the centers. You will find, however, that solving edges will be similar to learning F2L for you Fridrich solvers, or solving the 2x2x2 and expanding to the 2x2x3 for you Petrus solvers. When solving edges you will be required to make lots of small decisions and do some very fast thinking, the same as the intuitive steps I just mentioned. So bear in mind that this step will take a great deal more practice than the centers in order to get fast. Don't be discouraged by this, just bear in mind that this step is very important in the course of a solve, so it needs a lot of work to be made fast.
There are multiple methods for solving edges
You also need to know that there are lots of different methods for solving the edges of a 4x4x4, and I am going to try to list all of the ones that I know. However, you need to realize that I personally have one method that I prefer over all others, and I will advocate that method over all others on this page. I will give reasons and examples of why I prefer the method I do, but it is up to you to decide which method you want to use. Just bear in mind that these pages will consist of me teaching the edges method I use, but I will also be fair and show all the other edge pairing methods that I know.
For reasons that I will discuss much more in depth as you read on, I greatly prefer what I'm going to call the 2 pair chain solving method to any other edge method. I do, however, use bits and pieces of other methods for certain very special cases. Basically I don't think anyone should learn just one method and stick to it, it is much better to be a very well rounded cuber and know lots of methods so you can use the best of each one. I would say that I do about 90%-95% 2 pair solving and 5%-10% bits and pieces from other methods as special cases to speed up my solve.
6 pair solving vs. 2 pair solving
Here I want to address the issue of 6 pair vs. 2 pair solving. Basically 6 pair solving means you use a technique that places, as a goal, 6 pairs together at a time. Now this isn't always possible and sometimes you can only place together 5 pairs. However if luck is on your side you can place up to 7 or 8 together just by doing the 6 pair strategy. 2 pair solving is exactly that, you always solve two pairs at a time. Both methods have pros and cons, and to be honest nobody really knows if one method is faster than another, at least as far as I know. I actually use a combination of the 6 pair idea and the 2 pair idea, as I think it is better to combine methods than to just do one blindly. So on this page I'll list all the edge solving methods that I know, and you can choose how you want to combine them.
So if you're ready to get started choose the method you're most interested in. The way I solve edges is to use what I'm going to call 2 pair "chain" solving about 90%-95% of the time and bits and pieces of the 6 pair idea the rest of the time. Again please realize that some people use the 6 pair method 90% of the time and the 2 pair method the rest of the time, so my way isn't the only way. If you are interested in my method of solving edges please read the 2 pair "chain" solving page. If you are interested in the 6 pair method, I will be fair and provide a full example solve on that as well on the "other methods" page.