The method that I use for the 2x2, and is used my many other cubers, is the Ortega method. This method is very easy to learn and can be quite fast; my average is below 4 seconds for a 25 solve average with Ortega. Below will be the algorithms that I use, and tips on how to use then effectively and quickly.

Image Courtesy: Lance Taylor


First Layer: This is the first step in solving the 2x2x2 Rubik's Cube with the Ortega method. But to sum it all up in one sentence: First, make a full side (doesn't matter which colour, just the one that's the quickest and easiest to make), but not a layer. So, once you have a full side, not a face, you go on to orient the last layer with the following algorithms.


OLL: Adjust the upper face, (AUF), until you get the correct case as below and perform the algorithm. This will orient the last layer, and then you can go onto permuting both layers.

(R U R' U) R U2 R'	R U2' (R' U' R U') R'	R2 U2 R' U2 R2	F (R U R' U')[*2] F'	F (R U' R' U') (R U R') F'	F (R U R' U') F'	(R U R' U') (R' F R F')
Simple Sune case	Anti-Sune	Easy...	Sexy-Move twice	First half of the Y-perm	Sexy-Move once	Second half of the Y-perm

XLL: Once you're done with orienting the last layer, (OLL), you go on to permute both layers at the same time. After a bit of practice, your recognition of the following cases will improve and you will get a lot faster. The left image is the top layer, and the right image is the down layer.

(R U R' U') R' F R2 U' R' U' R U R' F'	F R U' R' U' R U R' F' R U R' U' R' F R F'	R2 U' R2' [y+U2] R2 U' R2'	R U' R F2 R' U R'	L D' L F2 L' D L'	R2 F2 R2
Simple T-perm	Simple Y-perm	Über easy...	Very easy...	Still, very easy...	No comment

Example Solves: This is going to be a few example solves solving with the Ortega method.

#1 Scramble: R F' R F2 R' F2 U R2 U'
First Layer: (z' x') U' R' U R
OLL: (U) R U R' U' R' F R F'
XLL: (y) R2 U' R2' [y+U2] R2 U' R2 (U')

#2 Scramble: U2 F' R2 U F2 U' R2 U2 R'
First Layer: R' B U' L U' L'
OLL: (U) R U2' R' U' R U' R'
XLL: (U2 y) R2 U' R2' [y+U2] R2 U' R2 (U)

#3 Scramble: R2 U2 F2 U' F' R2 F R' U
First Layer: (x) U' R2 U' R'
OLL: (U) F (R U R' U') (R U R' U') F'
XLL: R U' R F2 R' U R' (U')

#4 Scramble: F2 R F' U2 F2 U' F U2 R'
First Layer: (x' y) R' D R (z2)
OLL: (U') F R U R' U' R U R' U' F'
XLL: (U') R U' R F2 R' U R' (U')