HOW TO SOLVE A RUBIK'S CUBE: THIRD LAYER
Once you have completed the first two layers ("F2L"), hold the cube so that the white side is on the bottom. The white side will be on the bottom for the remainder of the solution. This means that the white side is the D side for all last layer algorithms.
Now look at the last layer face - there are 4 possible patterns of LL edges.
Pattern 1
Pattern 2
Pattern 3
Pattern 4
If you have a cross, move onto the next step. It doesn't matter if you have extra cubes on the corners; the minimum requirement is the cross.
Pattern 1
Skip this step because you already have the cross.
Pattern 2
Use F U R U' R' F' to form the cross if your cube looks like this
Pattern 3
Use F U R U' R' F' to form the cross if your cube looks like this
Pattern 4
Use F U R U' R' F' to form the cross if your cube looks like this. Then, your cube should look like patter 2 or 3. Then use the steps for either pattern 2 or 3 so that you will have the cross.
Tip: Notice how there is only one algorithm to memorize to create the cross on the third layer.
Orient the Corners
Move the corners to the appropriate places.
This cannot be drawn easily. Basically, this algorithm flips the corners on the right hand side. So you would rotate the cube and use the following algorithm until all the corners are in their proper spots: L U' R' U L' U' R U2
Example: If I needed to switch the top right piece and the bottom right piece, I would just use the algorithm.
Example: If I needed to switch the bottom left piece and bottom right piece, I would rotate the top layer once counter-clockwise and use the algorithm.
Example: If I needed to switch the top left piece and bottom left piece, i would turn the top layer twice (it doesn't matter clockwise or counterclockwise) and then use the algorithm.
THE STEP ABOVE IS ESSENTIAL; DO NOT SKIP IT
Flip the Corner pieces up
These steps will allow you to flip the yellow pieces up.
Your cube can have one of the following patterns.
pattern 1
pattern 2
pattern 3
pattern 4
Pattern 1
Pattern 1 is the pattern that all the other patterns lead to.
If you can, rotate the top layer (U) until the top face looks like this.
In order to complete this pattern, use the algorithm R U R' U R U2 R' U2 to flip all the yellow sides of the cubes up. If the cube looks the same, just repeat the algorithm until the whole top side is solved.
Pattern 2
If you can, rotate the top layer so that it looks like this.
If you can, use the algorithm R U R' U R U2 R' U2 to make the top layer look like pattern 3.
Pattern 3
Although the cube may have a plus, you have to move the top layer until the two yellow cubes are are on the left side. Then use R U R' U R U2 R' U2 to get pattern 1.
Pattern 4
Rotate the cube until the row of yellow sides are on top of the front layer as shown in the picture.
Then use the algorithm R U R' U R U2 R' U2 to return to pattern 1.
Rotate the edges
Rotate the cube in your hands until the solved edge is on the left. If there is no solved edge, use the algorithm R2 U' F B' R2 F' B U' R2 until there is a solved edge. To rotate the edges, on the top, right and bottom, use the algorithm R2 U' F B' R2 F' B U' R2 to rotate just the edge pieces clockwise. This solves the cube eventually as long as the edge piece on the left is already in its correct location. This may not work at first because it only rotates the edges clockwise once. You may need to do this again in order to solve the cube.
Congratulations
If you followed these steps correctly, you should have been able to solve the cube. If there are any errors, post them in the comments section.