Instructions
Choose a side to solve first. Any color will work, but the orange side will be used here.
Locate and place the orange edge pieces (the ones with only two sides) into the proper place by turning the layers of the Rubik's cube. Build around the orange center piece. The exact position of each edge piece is important. The edge piece with yellow on the non-orange side should be opposite white and orange piece, and in the same way, blue should be opposite green. When you are done, the top of your Rubik's Cube should be an orange cross.
Place the corner pieces (the ones with three pieces) into the proper positions by manipulating only the outside layers of the cube. You will not need to move any of the middle layers at all. Match the colors on the sides of the orange pieces. It is impossible to finish the cube if these colors do not match.
Put the center pieces in the correct place by moving the middle layer of the cube and then solve the rest of the middle layer. After aligning the center pieces, you will not need to turn the middle layer at any time during this process. You will need to temporarily break the top orange layer apart to do this, but you must always return those pieces to their proper place. Remember to put the middle pieces in the proper places (with both of the colors on the piece matching the colors of the sides).
Place the red, bottom corners into place by manipulating only the outside cube layers. The middle layers are not used in this step. As with previous steps, take care not to relocate any already placed pieces and put the pieces in the proper positions for all three sides. Continue to experiment until you find a set of movements that works for you.
Finish the cube by placing the bottom-edge pieces into their proper positions. You will need to move both the middle layers and the outside layer adjacent to the red side. No other outside layers need to be turned to finish the cube. Work with moving these layers without disturbing the rest of the cube until you have solved the Rubik's Cube.