Step 4: Position the Corners

You place the layer 3 corner pieces with move 3, which swaps the two top-right corners. Oddly enough, there are always 2 corners that can be placed correctly before you do the move. The trick is to find them.

Case 1: When one or no corners are correctly placed, turn the top layer and check again to get to case 2. Keep looking until you find them!

Case 2: When adjacent corners need to be swapped, orient cube with the bad corners at the top-right and do move 3.

Case 3: When diagonal corners need to be swapped, do move 3 twice, the first time with any face forward to get to case 1.