Instructions
Get all of one color on one side. Try getting all red on the top or front. Once you have all of one side it'll take some trial and error, but you'll be on your way to completing the puzzle the most simple way possible. To continue this method, go to Step 2.
Move the bottom of the cube until of the corners match the same colors as the blocks on the same corresponding top corners. Now you should be able to twist the middle sections of the cube to align the entire bottom and top rows to their appropriately matching colors.
Complete two opposite sides of the cube. This is easier then it sounds since you already have the bottom and top rows ready. You should also still have another side or the top of the cube completed with one color. If it's not, you may have made a mistake and should go back to Step 1.
Complete the final two sides that are left by twisting all of the middle pieces until all of the colors align for all sides.