This video shows you how to countersink a wood screw.
1. Find appropriate pilot hole drill. This should match the shank size of the screw.
2. Drill the pilot hole.
3. Locate a countersink with a single cutting edge or multiple cutting edges for a better finish.
4. Drill the countersink sink to the appropriate depth, stopping occasionally to verify fit by using the driver side of the fastener. If you need a flush fit, you are done. If you are going to fill the hole to hide the fastener, drive the countersink a bit farther so you have some area to work the fill material in.
5. Screw your parts together and you're done, or get the fill materiel and putty knife!
Alternately, you could use an all in one drill designed to pilot drill and countersink in one step, or use a specialty fastener with a self-drilling and self feeding tip, as well as a self cutting countersink.