3x3 - Beginner's Method
Cross
Make a cross shape for the bottom layer.
Only Case
Combination of R, L, F, B, U and/or D.
First Layer
Put the first layer corners in place.
Case 1
R U R'
Case 2
F' U' F
Case 3
R U' R' U2 R U R'
Second Layer
Put the second layer edges in place.
Case 1
(U R U' R') (U' F' U F)
Case 2
(U' F' U F) (U R U' R')
Last Layer Cross
Form a cross on the last layer.
Case 1
F (R U R' U') F' Fw (R U R' U') Fw'
Case 2
Fw (R U R' U') Fw'
Case 3
F (R U R' U') F'
Last Layer Edges
Swap two edges in the last layer. Repeat as necessary.
Only Case
R U R' U R U2 R' U
Last Layer Corner Orientation
Put the last layer corners in the right place by cycling three edges. Repeat as necessary.
Only Case
U R U' L' U R' U' L
Last Layer Corner Permutation
Apply the algorithm and repeat until a corner is correct. If there are more incorrect corners, move that corner into the top front right place and repeat.
Only Case
R' D' R D