2x2 - Ortega Method
Orient First Layer
Pick a colour and move all pieces so that the bottom face has that colour.
Case 1
Corner facing front. Move to bottom right corner facing down.
F' U' F
Case 2
Corner facing right. Move to bottom right corner facing down.
R U R'
Case 3
Corner facing up. Move to bottom right corner facing down.
U R2 U' R2
Orient Last Layer
Do the same for the top face with the opposite colour.
Case 1
F (R U R' U') F'
Case 2
(R U R' U') (R' F R F')
Case 3
F (R U') (R' U' R U) (R' F')
Case 4
(R U R' U) (R U2 R')
Case 5
(R U2 R' U') (R U' R')
Case 6
F (R U R' U') (R U R' U') F'
Case 7
R2 U2 R U2 R2
Permutate Both Layers
Move the pieces of both layers into their proper positions.
Case 1
(R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')
Case 2
x2 (R U R' U') (R' F) (R2 U') (R' U' R U) (R' F')
Case 3
(F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')
Case 4
z2y (F R U') (R' U' R U) (R' F') (R U R' U') (R' F R F')
Case 5
(R2 U' R2) (U2 y) (R2 U' R2)
Case 6
(R U' R) F2 (R' U R')
Case 7
(L D' L) F2 (L' D L')
Case 8
R2 F2 R2