The last layer is, unfortuanately, the hardest. But, unlike the first, requires very little thought, mostly just memorization. I suggest that you copy and paste the following tables into a word doc and print it off so you can always reference back to it. The easiest way to memorize moves is not to memorize the annotation, but to actually watch your cube(not your paper) as you do these moves and remember what they look like, which pieces go where, how should it look if you're doing it right. Certainly once you memorize them you can show off to your friends, but you dont want to go B R'L B L', you want to see how the cube looks. It may seem harder at first, but not only is it better but it is easier to memorize. Okay, and now for the fun part. Before you start the moves, you should turn the cube upside down so that the color you started with is now the D face and the last layer is the U face, all moves will be annoted this way.

When something is in the right spot, it is where it goes on the cube, it is positioned correctly. Correctly positioned pieces may not be "twisted" the right was though (they are in the right spot, but their stickers don't match the middles they touch). If a piece does match the middles it touches, then it is oriented correctly. Pieces must be positioned correctly in order to be oriented correctly(duh), but not all positioned pieces are oriented correctly. Keep in mind these terms.

Positioned
In the right spot
Oriented
In the right spot and matching the middles
    The steps for doing the last layer are:
  1. Make a cross on the bottom
  2. Position the corners
  3. Orient the corners
  4. Orient the edges

First, we have to make a cross on the bottom. There are four possibilities for the bottom edge pieces to be. There can be two adjacent edges that need flipped, two oppisite edges that need flipped, all edges need flipped(there are four left), or none need flipped and the cross is already formed. Obviously, if the cross is already formed, skip this step, and move on. Here are the moves for the other three. Ignore the corners, worry about the edges. This is what your U face should look like.

Now that you have the cross, the next step is to position the edges. This is the step that most people are confused by, but it is actually the easiest of the last layer once you get it (and only one algorithm if you dont count the repeat!). First, find two adjacent corners on the last layer that share a color (other that the last layer's color). Turn the last layer so that these corners are both on the face of the color that they share. Check to see if the are positioned correctly. They do not have to "look right", they just have to be in the right spot to be positioned correctly. Then check the other two corners.If either of these sets need switched, turn the cube so that the wrong corners are facing you and do this move:

 B U'F'U B'U'F U2
. If all the corners are wrong, position two that need flipped facing you and do that move twice w/o the U2:
 B U'F'U B'U'F B U'F'U B'U'F
Now, your corners should be positioned correctly (not oriented).

The next step is to orient the corners. There are six positions that the U face can be in. First turn the cube so that the U face looks like one of the pictures below, then do this move: 

 R U R'U R U2 R'U2
. Then, reposition so it looks like one of the top layers and repeat. The first picture of the six (applied either once or twice) will complete the step. Pictures 2-5 will get you to move 1. Afterwards, your corners should all be oriented correctly, and the U face should be a solid color .

The last step is to orient the edges of the U face, thus completing the cube. There are four possible positions for the cube to be in, one of them is solved. I will provide the other three. The arrows on the diagrams indicate how you are moving the edge pieces, it is implied that the U face is complete. After this, the cube should be solved. If it isn't, it is likely that you screwed up one of these last, long moves and that you destroyed the cube completely. Don't worry just start over and be careful. Otherwise, rejoice! Then memorize the algs and go win a lot of bet money off your friends =).

Note: If the cube is not solved, you may need to do this move again.
Note: Instead of this move, you can also just do the first move once, which will give you picture one. Then do that same move once or twice to solve. This method takes more time, but you only have to know the first algorithm.
Note: Instead of this move, you can also just do the first move once, which will give you picture one. Then do that same move once or twice to solve. This method takes more time, but you only have to know the first algorithm.

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