If you've made it to this page then I assume you're interested in learning some of the strategies for seeing these extended cross solves. This page is an attempt to present some of the main strategies I use when looking for the shortest extended cross solve.
The 2x2x2
If you, like I was when I first tried this method out, have only ever done "cross" methods then chances are you're very unfamiliar with solving the 2x2x2. If you already use a 2x2x2 system then go on to the next section. So if you have only ever solved the cross, or some other method, then you will want to familiarize yourself with solving the 2x2x2. Some basic strategy for doing this is to 1) form a 2x1x1; 2) form a 2x2x1 out of the piece create in #1; 3) form a 2x2x2 out of the piece created in #2. Here is an example,
Here we have only the pieces necessary to form the 2x2x2. We can solve the 2x2x2 from this particular position in 6 moves. If you can see this solution that's great! If not, then let's step through it. For each step use the "original position" cube to try to follow along and see how each step relates to the original position. If you click on a center piece of a face you can even do the same moves on the original position cubes. Hold down alt while clicking to rotate the opposite direction. For each step, the cube in the right column starts in the final position as the previous right column cube, only with a new piece added each time. This way you can see the step-by-step approach I take to figuring out how to solve a 2x2x2.
It should now be fairly obvious what the strategy is to solving the 2x2x2. First you want to try to find the fewest number of moves to put together a 2x1x1. Once you find one, can you find an easy way to extended your 2x1x1 into a 2x2x1? If not, then try to go back and choose another pair to build your 2x1x1. Once you find a 2x1x1 that easily extends into a 2x2x1, try to find a way to place the last edge to form your 2x2x2. Once you have a solution, try to find ways to do two things at once. Use the above example as an idea. We were able to form the 2x2x1 and place the last edge all in one move, leaving the last turn to just simply form the 2x2x2 by lining up the two pieces. This extends as a general rule. Once you have your solution, can you combine steps to help shorten the number of moves? Later you may find other ways on your own to solving the 2x2x2, the way suggested here is certainly not the only way, it is just a good way to try and get started if you have previously no experience with the 2x2x2.
Extension from 2x2x2 into extended cross
By now you should be fairly comfortable with solving a 2x2x2 on your own if you were not originally accustomed to it. Now what you want to try to do is to solve the 2x2x2 while paying attention to the other two edges of the first layer. A beginning strategy to this step is to try to find the shortest solution to the 2x2x2, that you would use if you were ignoring those other two edges. Then go through that solution in your head and see if the moves will put the edges in a bad position. A "bad position" is one that will take generally around 5 moves to solve the last two edges, in addition to the number of moves it took you to do the 2x2x2. So you can see if you get a 7 or 8 move 2x2x2 and you have a 5 move position for the last two edges, then you've now done 12-13 moves on the extended cross, which though not terrible, is not that great either. What you want to do is end up in a position where it may take only 2-3 moves. Later you can try to extend to solving the 2x2x2 and one edge as a direct solve, while paying attention to the last edge and therefore trying to get it into a "good" position after completing the 2x2x2 and one edge. These are all good strategies to use all the time, since sometimes solving the 2x2x2 and then the last remainging edge or edges is indeed the fastest way. However, don't limit yourself to using this strategy every time.
Direct solving the extended cross:
If you really want to learn the extended cross method in a way that will truly be useful to you later, you have to learn to direct solve it. Basically all I can say about this step is that you have to become so familiar with the process of following all 6 pieces in your head that it becomes just as easy to solve the extended cross as it does the cross, or the 2x2x2 for you. Naturally it will always be a little bit more difficult because there are 6 pieces instead of 4, however I've noticed that when I've practiced extended cross solves a lot I can usually see a decent solution (around 10-11) moves for most all scrambles. This method is still in the works, but my eventual goal is to average under 10 moves for each scramble, and to be able to do these solves smoothly going "slow-fast" during the F2L. If I come up with any new ideas I'll post them, but so far you know now as much as I know about the process. The rest comes with practice and determination. I hope these pages have helped you understand the extended cross method if you're interested, or at least cleared it up for you if you're not. If you have any more questions or comments then feel free to e-mail me at foozman17@hotmail.com