Countersinking a screw is useful when trying to hide the head of a screw from view, or when the screw is not long enough to make a solid connection with both pieces of wood (or other material).
1. Measure the diameter of the screw you will be using. Also measure the diameter of the head of the screw.
2. Choose a drill bit that is slightly smaller than the shaft of the screw, and another drill bit that is slightly larger than the head of the screw. As seen here.
3. Mark on the piece of wood where you will be drilling the hole. As seen here.
4. First, drill the pilot hole with the smaller drill bit. Then, drill the larger hole, but only as deep as you need to countersink the screw. Note in this picture that the larger hole is not nearly as deep as the smaller pilot hole.
5. All that remains is to put the screw in.