Layer 3: Part 1

By now you should have something looking like this:

cube2-14 cube2-13 cube2-12 cube2-15

Right, now flip the cube so the final layer (opposite you first solved) so that it faces up. In this part will will get the corner pieces into the correct positions. For this, you need to remember that each cubelet has one position, but may be in a different orientation than required. So, get the cube into one of the following positions, or rotate the layer until it is...

1234
cube3-1 cube3-2 cube3-3 cube3-4

Now turn the whole cube so that the final layer sits on the top of the cube. Then do the moves relevant to the situation the cube is in

1

leftup topleft rightup topright leftdown topleft rightdown topright

2

topleft rightup topright leftup topleft rightdown topright leftdown
NOTE: Notice that this is the opposite to 1.
This could also be achieved by doing 1 twice.

3

Not exactly needed, as you can get to 1 or 2 by turning the top layer... look at the moves- they are very similar, but from a different view point :)
frontCW topright backCW topleft frontCCW topright backCCW topleft topleft

4

If you do 1 on this, you will also be able to do 1 another one or two times to achieve the same result instead. This can be usefull if you can't remember all these cases.
rightup backCCW topleft backCW topright rightdown topleft

So hopefully you see that this part isn't terribly hard, you can solve it using one set of moves. But if you want to be good at it i advise learning at least 2 and 4 to make things quicker.

You should now have a cube with 2 layers completely finished and the corners in the right position in the final layer, but not necessarily the right way around.