It's time to turn on the colours again. The first thing to do when you arrive at solving the corners is to choose two corners that have a common colour. In this diagram, you can see two greens.

Let's turn off the edge colours to make things a bit easier to understand. There's the two corner pieces with green on them. They are next to each other.

Actually, on the other side of the cube, the two reds are together too. It doesn't matter what pair you pick. So let's choose the reds.

Turn the white face until the two corners with red are nearest to the red face. If you look here on the red face, they are both in the wrong place. The red and yellow cubie should be where the red and green cubie is, and vice-versa.

If these two are the only two that need to be swapped, and the other two corner cubies are ok, then you need to perform the following move:

F U-1 B-1 U F-1 U-1 B U2

If both corners need swapping at the same time (as in this case) use:

R U2 R-1 L-1 U R U-1 L U2 R-1 U2 (thanks to ~bur-c~ and Tony S for pointing out the error here)

For this example, assume the F is the orange face, U is the white face, L is the yellow face, B is the red face, and R is the green face.