The Yau method is currently the fastest method in solving the 4 by 4 Rubik's cube. When using this method, it only works on the centers and edges steps of the 4 by 4. For the 3 by 3 step, you can use the fastest method that you know for 3 by 3. When using the Yau Method, your first cross will already be solved when you go to 3 by 3 mode. There are 6 very easy and fast steps for this method. Go HERE for a full Yau Method tutorial. You could also look through the rest of this page.
When you solve the first 2 centers, they have to be opposite from eachother. In this example, we will be solving the white and yellow centers as the first two. You can solve them however you can, but if you want to learn to solve them faster, you can watch videos on 4 by 4 example solves.
In this step, you are going to solve 3 edge pairs. You have to make sure you solve the edge pairs that are the same color as one of your first centers. So, when you solved the white and yellow centers, you now have to make 3 edge pairs that have white in them. (it doesn't matter which edge pairs as long as they have white in them) You can make them the same way as you do with the beginner method. After you have made them, insert them onto your white center. (be sure to put the edges in the correct spot (color scheme))
This is one of the more difficult steps to comprehend. You have to solve the last 4 centers without ruining your edges that you made in step 2. When you make the centers, remember to put the centers in the correct spots (color scheme). For how to do this, watch THIS
This step is really easy. You can just solve the last white edge pair like you do with the 4 by 4 beginner method. After you have made the edge pair, you can insert it into the white cross. Before you move onto the next step, make sure all the centers are aligned with the cross edges.
You technically could solve the rest of the edges like you do with the beginner method, but most people that use the Yau method use something called 3-2-3 edge pairing. 3-2-3 edge pairing is a VERY fast way to solve the rest of the edges, and it isn't even very hard! If you want to learn 3-2-3 edge pairing, watch THIS.
For this step, you just use the fastest method that you know for the 3 by 3. If you want to learn the fastest method on the 3 by 3 Rubik's cube, you can go to the CFOP page on this website. You may get a case that you don't know. That is called parity. There are 2 parities (an OLL and a PLL parity). For how to solve them, scroll down.
This is the OLL parity. You solve both OLL parities the same. You recognize it because when solving the yellow cross you have a non-3 by 3 case. (not line, angle, or dot) It is when you have 1 or 3 incorrect edge pieces.
To solve it, hold 1 of the incorrect edges at you, then do this algorithm: (All R, R', and L moves are with 2 layers) R, U2 make the face on the bottom at you, R U2, R, U2, R', U2, L, U2, R', U2, R, U2, R', U2, R'
This is the OLL parity. You solve both OLL parities the same.You recognize it because when solving the yellow cross you have a non-3 by 3 case. (not line, angle, or dot) It is when you have 1 or 3 incorrect edge pieces.
To solve it, hold the incorrect edges at you, then do this algorithm: (All R, R', and L moves are with 2 layers) R, U2 make the face on the bottom at you, R U2, R, U2, R', U2, L, U2, R', U2, R, U2, R', U2, R'
You solve both PLL parities the same. You can recognize this by when your cube won't solve. It can look like in image 1, where there is 2 incorrect edges next to each other. It can also look like in image 2, where there is 2 incorrect edges across from each other.
To solve it, hold one of the not solved sides at you, yellow up, (example: in the picture above, hold the side with the red center and 2 green pieces at you), and do this algorithm: 2R2, U2, 2R2, u2, 2R2 u2.
You solve both PLL parities the same. You can recognize this by when your cube won't solve. It can look like in image 1, where there is 2 incorrect edges next to each other. It can also look like in image 2, where there is 2 incorrect edges across from each other.
To solve it, hold one of the not solved sides at you, yellow up, (example: in the picture above, hold the side with the red center and 2 orange pieces at you), and do this algorithm: 2R2, U2, 2R2, u2, 2R2 u2.
If you still want to get faster at the Yau Method, you can learn 3-2-3 edge pairing, half centers, and getting faster at parities. Go HERE for a link to how to do all that.