The Sergs.B. uses the most common method of solving the Rubik's cube. The basic idea is to solve it layer by layer. First we solve the top, then the middle, then the bottom. Here's a version of what he does in the video (this is not what he does in the video, but a description of what he describes in the video, but typed):
The first thing we need to do is solve the cross on the first layer. You can use any color you want for the first layer, but for this we will use green. So we will look on the bottom layer for a green edge cubie. When(if) we find one with the green facing down, we'll move the bottom as many times as we need to get the color that is not green to its center color. When we do that, we simply move the front twice. This will put in the first cubie. Look to see if you have any more cubies on the bottom. If you have one that has the green facing the bottom, you can bring it to the second layer (he doesn't say this in the video). If there is a cubie on the second layer, we'll just bring it to the third, in such a way that the green is facing down. Now we simply move the bottom until the not-green color matches up with the center color. Then we just move the front twice and it's in! If one is in the wrong spot on the first layer, you can move it down twice, repeat the steps you did for every other one. Now you should have the cross solved. For the corners, we must first find them. Look on the bottom layer for one that is in optimal position, with the green not facing the bottom. If we find one, we line it up with it's colors, again looking at the centers. Next, we make the green face us, and do this: move it away- move the bottom layer to the opposite direction that the cubie is right now(making sure the green faces you), Bring it down- bring either the left of the right side down, so that you can put it in- move the cubie that we are trying to put in into the right spot and finally, bring it back up- bring the side that you brought down back up, with the cubie that you put in. Do this for any more cubies that are in the optimal position. If a cubie is on the bottom layer, but the green is not facing you, do this: move the cubie to a spot where (if it was possible) it could jump up to the spot it's supposed to be in. Next, turn the entire cube so that the cubie we're focusing on is on the right. Now, we bring the right down(cubie now on bottom layer), move the bottom twice, and bring the right up. The green should now be facing you, and you can put it in. You may run into a case where you have a cubie in the top layer, but not in the right position. To fix this we will simply bring it out. To do this we make sure that the cubie we're getting out is on the right side. Next, we bring the right down, move the bottom to the left, and bring the right back up. Now it's a simple matter of getting it in. If you're having trouble, don't worry! Try it for a few minutes, then email me if you still can't get it!