Step by Step Solution
Now that you have a language to understand the movements of the cube, we can begin solving it. Recognize that each side of the cube has a central cubie that does not move. The rest of the cubies revolve around this center. In a standard 3x3x3 Rubik's Cube, the central cubies are labeled white opposite yellow, red opposite orange, and blue opposite green; however, you may have a cube with different colors. This isn't a problem just get familiar with the centers of your cube, but, for this tutorial, I'm going to use the color scheme of a standard Rubik's Cube.
Step 1 - Forming the White Cross
We want to build a white cross on the white side, so turn the white side, or the side with the white central cubie, towards you. Now find the center edges. These pieces only have two colors on them. The ones we are looking for will be the white cubies that sit directly next to the central white cubie and form a cross. Their color schemes will be red/white, blue/white,green/white, and orange/white. Match one of the white centers of the middle edges to the central white cubie. So, for example, the red/white middle edge goes to the white center. Now turn the white face of the cube so that the red/white middle edge matches the red center. Now you should have one extension of the white cross matched with its corresponding center. Do this for the remaining middle edges, you might have to move some correctly placed pieces in order to move in another correctly placed piece. Don't sweat it! Just remember how and where you moved the originally placed piece and place it correctly again.
Step 2 - Completing the White Side
Now you have your cross, and we want to use this as a reference point. So, make the white cross the Down face or position the cube with the yellow side facing up. Our objective now is to find the white corner pieces. Their color schemes will be orange/blue/white, orange/green/white, red/blue/white, and red/green/white.
The white corner pieces can only be on the corners of the cube, so look around for them and find out how they are positioned. You want to pay close attention to the white part of the corners. The white stickers may be facing left, right , or up. Ideally we want the corner white pieces in the top layer with their white stickers facing left or right, but, more than likely, they won't all be facing left or right or in the top layer. If you do have some corner white pieces in the top layer with their stickers facing left or right, notice the color of the sticker opposite the white one.
Let's say that the corner piece you found with the white sticker facing horizontally is the red/blue/white, and the blue sticker is facing horizontally as well (making the red sticker face up). Turn the U layer so that you match the blue corner with the blue center, and face the blue side towards you. The white sticker should be facing your right. If the sticker is facing right, perform this algorithm:
R U R'
If the white sticker is facing left after the corner and center has been matched use this algorithm:
L U L'
Position the cubies so that the white stickers are in the top and facing left or right. Try not to focus on the algorithms as much as the logic of the movements. Continue to solve the corners of the white side.
Step 3 - Solving the Middle Layers
So you've completed the white side of the cube. From this point on, the white side will be your bottom layer. Now we want to complete the middle layer, and we are going to use two main algorithms to do this.
First, locate the middle-edge pieces. They will have two colors and their color schemes will be orange/blue, orange/green, red/blue,and red/green. As long as these middle-edge pieces are in the top layer, we don't care how they are oriented; however, if they are in the middle layer already and incorrectly oriented, we will have to move them.
Let's take care of the middle-edge cubies in the top layer. Match the horizontally facing sticker with its center. So, for example, you notice that on the orange/blue middle-edge piece, the blue sticker is facing horizontally (towards you), and the orange sticker is facing up (towards the ceiling). Now the orange/blue cubie must move left. Use the following algorithm to correctly position the orange/blue cubie:
U' L' U' L U F U F'.
Now let's consider the opposite case. Perhaps we have the same middle-edge piece in the top layer(orange/blue), but this time blue is facing horizontally, and orange is facing up. Turn the top layer so that the orange sticker of the middle-edge piece matches the orange center, and face the orange side towards me.
The algorithm you will want to use in this instance is
U R U R' U' F' U' F.
This should correctly position the orange/blue middle-edge piece also.
Finally, you may have middle-edge pieces in the middle layers already, but they might be incorrectly oriented. In this case you will need to use a transformation of the above algorithms to move that middle-edge piece into the top layer:
R U' R' U' F' U' For
L' U L U F U F'
Step 4 - Forming the Yellow Cross
O.K., now we are ready to tackle the final layer (remember to keep the white layer on the bottom). We start just like we did at the beginning with the White cross, except now we will form the Yellow Cross. This is easier said than done since 2/3 of the cube is already solved for. We will need to use algorithms that don't disturb the rest of the solved layers.
You want to look out for three patterns on the yellow side, only worry about the middle-edge portions of the yellow cross (the ones that match directly with the yellow centers, not the corners).
The first pattern you might find is that there is no pattern (no parts of the yellow cross are completed).
The second pattern is an L(or the upper/lower, left/right portion of the yellow cross).
The third pattern you might find is a straight line of yellow stickers (the middle portion of the cross).
All three patterns use the same algorithm, but we have to orient the patterns in certain ways. For the pictures above F will be the orange face. The algorithm is this:
F R U R' U' F'
If we have the first pattern, then it doesn't matter how the yellow layer is oriented, we can just perform the algorithm. If we do that, it should give us the second pattern. If we have an L shape we want to turn the top layer of the cube so that the L is backwards. It will look like the upper left portion of the yellow cross. Once we have this pattern we perform the same algorithm, which will give us the final straight line pattern. Rotate the yellow side until the line of yellow cubes forms a minus sign (-). It will be the middle portion of the yellow cross with no top or bottom. Now perform the same algorithm, and you should have the yellow cross. You might have more than yellow pieces facing up, but for now we want to worry about the yellow cross only. Note the middle-edge pieces of the cross might not match up.
Step 5 - Solving the Yellow Layer (Kind of...)
Now all we need to do is solve the yellow corners. Again we are looking for yellow patterns, but this time the patterns involve the yellow corners. Ideally we want a pattern that has the yellow cross and one yellow corner facing up. But we will probably have a blank yellow cross or a yellow cross with two yellow corners facing up (these corners may be corners on the same edge or catty-cornered on different edges).
If we have the ideal pattern of the yellow cross with one upturned yellow corner, then we want to rotate the top layer until this yellow corner is in the bottom left of our yellow face. Now we want to perform this move:
R U R' U R U2 R'
Likely this will give you the same pattern of a yellow cross with one upturned yellow corner. Rotate the top layer again, so that the upturned yellow corner is in the bottom left portion of the top layer and repeat the algorithm. This should solve the yellow side, but the edges will still be mismatched.
Now what if you don't have the ideal pattern. In this case, you will use the same algorithm. If you have the pattern of the yellow cross with two upturned corners that are a part of the same edge, then you must rotate the top layer until the cube looks like a fat T (the two bottom corners of the yellow cross will be unsolved and the two top corners will have the yellow stickers facing up). Use the algorithm when the two solved corners are on the top and the unsolved corners are on the bottom.
If the two upturned yellow stickers are catty-cornered from one another, ignore one of the corners and treat this case like the ideal situation (only pay attention to one of the upturned yellow corners and rotate it in to the lower left portion of the cross).
You might find that this step is tedious because it takes a few times to get the ideal pattern. If all else fails, just keep using the algorithm. It should give you the ideal pattern, and you will get the yellow layer facing up.
Step 6 - Solving the Corners
If you have any corners that can be matched with their sides (two corners of the same edge that are correctly oriented), go ahead and rotate the top layer of the cube to match them with their sides. If not just use the algorithm until you can get two corners of the same side that are correctly oriented. When you have two corners matched, position the cube so that the matched corners are facing away from you. So for example, if you have two green corners that are matched, the blue side will be facing you. When you have these two corners use this algorithm to orient the remaining corners:
R' F R' B2 R F' R' B2 R2
Step 7 - Solving the Middle Edges
This is the final step. You should have 4 correctly matched corners, and 3 or 4 incorrectly matched middle edge pieces. If you have 4 incorrectly matched middle-edges, use the algorithm below until you have 3 incorrectly matched middle-edges. If you have 3 incorrectly matched middle-edges, reposition the cube so that the correctly matched middle edge is facing away from you. For example, if the orange side was completely solved, the red side would face me.
For this algorithm, we need to see which way the middle-edge we are solving for is going. If it is going to the right, then we will use this algorithm:
F2 U' R' L F2 R L' U' F2
If the middle-edge is going to the left, then we will use a transformation of the algorithm:
F2 U R' L F2 R L' U F2
Notice all that changes is the U movement. Congratulations! You solved the Rubix Cube.