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!
Now that you have the whole top completed, you are ready to move on to the bottom. This is probably the simplest layer, and can be repetitive. But that's just as well, as practice makes perfect! To start off, we need to find a color that is not green, as green was our top layer's color. Next, we line up the color facing us, making it so that it's lined up with it's center color. Now we look at the color that is not lined up with it's center color (the other color on the cubie). With that we know if it needs to go up and to the left, or up and to the right. If it needs to go to the right, move the bottom to the left, bring down the right, move the bottom back to the right, and move the right back up. Now it's a simple matter of getting the green(or your top color) up to the top again, so remember, move it away, bring the right down, put it in, bring it up. This puts in an edge cubie. Do this for the rest of the cubies, and remember if a cubie has the bottom layer color, ignore it's taunting. We have nothing to do with it right now. Also, email me if you're having trouble.
Now you have two thirds of the cube completed. To continue to the third and final layer, flip the whole cube over. Now you're last layer should be on top, and it will now be referred to as the top. For this layer, we focus once again on the cross. I'll be describing the circumstances in order, so I'll be starting with the circumstance of just having the blue dot in the middle, no edges on the blue side flipped over so we can see the blue. So, if we have the blue dot, we do this: move the front (clockwise), the top (clockwise), the right (clockwise, or up), the top counterclockwise, the right down(counter-clockwise), the front down, so the first solved side aligns back up once more (counterclockwise). Now you have a strait line. Move the entire cube so that the line is horizontal. Do the algorithm again. Now you should have the L in the top right corner. Move the entire cube so that the L looks like a backwards L, or so that it's hugging the top left corner. Do the algorithm again. Now you should have the cross. But if you'll notice, the edges aren't aligned with their center colors. If they are, hang right, I'll get to what you need to do in a minute. If you don't have edges aligned, move the top layer so that two of the edges do align with their corresponding middle. If you have two that are across from each other, do this: Move the entire cube so that one of the "solved" edges is on the left, and one on the right. Now bring the right up, move the top clockwise, bring the right back down, move the top again, bring the right up again, move the top twice (clockwise or counter, it doesn't matter), bring the right down again, and the top clockwise. The two layers should not be disrupted. Now you should have done what looks like messed up the edges that you had, and that's pretty much correct. But move the top twice, and you'll notice that two other edges are "solved". Move the entire cube so that the two "solved" cubies are hugging the top hugging the top right corner. Do the algorithm again. You now have the cross correctly done. Now we may move on to the corners. If you find one that is in the correct position(it does not have to be oriented), You can put that in the bottom right corner. But don't move the layer, move the entire cube. If you cannot find one just choose a random one, and do this anyway: move the top clockwise, bring the right up(clockwise), move the top back to the right (counter-clockwise)bring up the left (Counter-clockwise), bring the top-back to the left(clockwise), bring the right back down, move the top back to the right(counter-lockwise), and bring the left back down(counter-clockwise). Now you might have at least one corner in the correct position(once again, they do not have to be oriented correctly!). If you have one, put it in the bottom right corner, and do this algorithm again. Had one before, and still don't have the others? Do the algorithm one more time, and that should do it. If it doesn't work, you're doing something wrong. Now that you have the corners in th right spot, it's time to orient them. This is the final step. Find an unoriented corner (if you don't know what oriented means, click here), and put it in the bottom right corner, by moving the entire cube. Now we do this: bring the right down(counter-clockwise), move the bottom to the left, bring the right back up (clockwise), bring the bottom back to the right. It now looks like I screwed you up. Don't panic, do the algorithm again. The cube still looks bad, but trust me. If the corner is now oriented, move the top, and the top only, until you find another unoriented corner. Repeat this algorithm, until the cubie is oriented. If the cube is not solved, move the top again, until you find another unoriented piece, and do the algorithm to this piece too. If it is not solved, you did something wrong. Try again (don't give up!!), watch the video, follow along, and/or email me. Don't give up, and as always: Think of it logically.