The Ortega method is faster than any beginners method but it is not as fast as the EG or CLL methods. (EG is the fastest method) With practice you can get sub 10 seconds with this method. You start by solving a side (probably the one mostly finished) then you do 1 algorithm to solve the second side. After that, you do 1 algorithm to solve the cube. You should already know the beginners method for the 2 by 2 before learning this method.
Solving the first side is easy and you can solve it in a decent time with practice (you are supposed to know how to solve the cube using the beginners method so this should be easy). One thing that you might want to know, is that you don't have to get the first layer. This makes it much faster than the beginners method.
For this step, you are going to solve the 2nd side. You will get one of the cases shown below. You can either do a 2 by 2 Ortega algorithm (shown below), or you can do a 2 look 3 by 3 OLL algorithm. If you already know 2 look 3 by 3 OLL, you can use the same algorithms for most cases, except ignore making the 2nd cross step. The Ortega algorithms are faster and easier though. Note: for the following cases, you may have to turn the cube to recognize the case. If this doesn't make sense press HERE for a video on how to do it.
The cases are written below and you hold it like shown in the picture. The pictures are of the 2nd side. In the pictures shown, you are solving from white to yellow. You then look at where the yellow stickers are recognize your case. Then you do the algorithm that is written next to your case. It will explain anything tricky but the moves will be written in letters. If you don't know how to read moves, go press HERE for a link to the the cube notations page.
If this does not make sense press HERE For a link for a video on how to do it.
In this case you hold the cube like this and do R, U2, R', U', R, U', R'. This will solve you second side.
This case you do a algorithm from the beginners method on 2 by 2 and 3 by 3. You do R, U, R', U, R, U2, R' to solve you second face.
In this case you do this algorithm from this position, R, U, R', U', R', F, R, F' and that will solve your second side.
For this case, you hold the cube like shown and do the algorithm: F, R, U, R', U', F'.
For this case, you hold like shown and do the algorithm: F, R', F', R, U, R, U', R'.
For this case, you hold like shown and do this algorithm: R2, U2, R, U2, R2.
For this case, you hold the cube like shown and do this algorithm: F, (R, U, R', U',)2 F'. But, you could also do the bowtie or L algorithm from 2 look CFOP if you already know that.
For this step, you are going to finish off the cube. You are going to look around for bars on the unsolved sides. A bar is when 2 colors match up next to each other horizontally. You also should be on the look out for a full side and/or layer. After you have recognized your case you do the algorithm shown. The colors of bars and such, will not always be the same as shown. The colors can be different. If some area is blank, it doesn't matter what that color is.
In this case it shows (in the picture) both sides that you have already solved. It is where you have no bars. Bars are 2 pieces of the same color matching up horizontally. Then you hold the cube with any solved face up and do R2, F2, R2, to solve the cube.
This is shown like the case above (look there if you didn't read it). The white side cane be your first or second side you solved, you hold the layer on the bottom and you do this algorithm, F R U' R' U' R U R' F' R U R' U' R' F R F' and that will solve your cube.
In this case you have 1 bar and you have already solved the white and yellow side. You hold it with the 1 bar on the top of the side at you, and you do this algorithm, R U' R F2 R' U R' and that will solve your cube.
This case is when you have 1 full side (other than the first 2 sides you solved), and vertical bars on every other side. For this case, you hold the 3rd side you have solved at you, and do this algorithm: R2, U', B2, U2, R2, U', R2.
This case is very common, and you hold the 2 bars on top of eachother. You hold the side with the 2 bars at you, and the first 2 sides you solved on the top and bottom. Then, you do this algorithm: R2, U', B2, U2, R2, U', R2.
For this case, you hold the layer on the bottom, and the 3rd side you solved on the left. On the top and bottom are the first and second sides you solved. Then do this algorithm: R, U, R', U', R', F, R2, U', R', U', R, U, R', F'.