I typed this up to show as an example of an ALGORITHM. What is below is all based on Dan Brown's youtube videos.
Notation: -------- F = Front side of cube (facing you) U = Upper side L = Left side R = Right side D = Down side green side = side with green in center white side = side with white in center etc... center piece = piece in center of a side corner piece = pieces at the corners edge piece = not center or corner pieces
Algorithm Notation: ------------------ F = turn front side clockwise by 90 degrees F' = turn front side counter-clockwise by 90 degrees U = turn upper side clockwise by 90 degrees U' = turn upper side counter-clockwise by 90 degrees 2U = turn upper side by 180 degrees (clockwise or counter-clockwise...it doesn't matter) R = turn right side clockwise by 90 degrees (clockwise, as if you were facing it) R' = turn right side counter-clockwise by 90 degrees etc...
1. Solve the green side first > start with green side up > find a green edge piece and move it to the Down side > rotate Down side until other color on the edge piece matches the center piece > now twist side 180 degrees to get green edge on green side > if it's all OK, move on to next edge piece > if edge is in correct spot but flipped, do F' U L' U'
at this point, after getting all 4 green edge pieces in place, you should have the green cross on top and all edge pieces should be correct
> fix green side corners: > find a green corner and get it directly under where it should go (match the other two colors on the corner piece to the other two side colors) > with the piece you are working on in the bottom right corner, do R' D' R D from 1-6 times (keeping the same face forward at all times) > once that corner is done, solve the other 3
at this point you should have the green side done and all of the first layer done (and all edge pieces matching their correct sides)
2. Solve the second layer... > turn green side down, blue side up > find an edge piece without blue in it (see ** if can't do this) > twist the top blue side so edge piece matches side color > with that piece front and center, look for which side (left or right) matches top color and do one of these: top matches right side: U R U' R' U' F' U F top matches left side: U' L' U L U F U' F'
> repeat for all edge pieces of second layer.... ** if you can't find a top edge piece without blue in it, find one that is an edge piece in the middle layer and make it the front-right-middle, then do this: U R U' R' U' F' U F at this point you should have two layers done!
3. Solve the BLUE CROSS.... > look at top blue layer for one of these cases: no small L: do F R U R' U' F' to get small L small L: make it top back left, do F R U R' U' F' the "L" you are looking for is made up out of three blue pieces, the center and two edge pieces
you should now have three in a row. make the 3-in-a-row go left to right across the top
and again do F R U R' U' F' to get blue cross
> try twisting top blue side so two edge pieces line up with their correct sides if you can't get two lined up do R U R' U R 2U R' if you get two lined up, and they are across from each other, make the lined-up edges the front and back sides and do R U R' U R 2U R' (this should make the two lined-up sides adjacent) if the two lined up are adjacent, make them the right and back sides and do R U R' U R 2U R'
should now have blue cross on top and be able to twist top to get all edge pieces lined up
4. solve the final 4 corners!!! > check the corners to see if they are in their correct locations (even though they may be flipped). You should either have 0, 1, or all 4 in their correct spots.
if 0: do U R U' L' U R' U' L with blue cross on top this should get 1 or more corners correct if 1: do U R U' L' U R' U' L with blue cross on top and correct corner as upper right of front face this should get 4 corners correct, but you may need to repeat this U R U' L' U R' U' L once if 4: go to next step...
> with 4 corners correct (but flipped), pick a side and make it the front, with a corner to flip in the top right
NOTE: always keep this front side the same during the next few steps!!!! do R' D' R D twice and see if that corner is flipped correctly if no, do R' D' R D twice again
if yes, turn up face 90 degrees (U) and repeat with next corner (if needed), always keeping the same front face (even though it looks like you're messing things up!)
NOW TWIST THE TOP AND THE CUBE IS SOLVED!!!