Creating an attractive finish on woodworking projects requires concealing the fasteners from view. You can completely hide screws in a wood dowel with a process called "countersinking," where the head of the screw is set below the surface of the wood. Countersunk screws are installed in a conical-shaped hole cut into the wood with a specially designed drill bit. The area over the screw can then be disguised to hide the screw and the hole from sight.
Drill a shallow hole in the dowel with the countersink drill bit. Drill into the dowel only far enough so the head of the screw will be set below the surface of the wood. However, drill deep enough into the dowel so there will be enough space left in the hole, above the head of the screw, to accept the wood filler. A rule of thumb suggests making the depth of the countersink hole three times the thickness of the head of the screw. Test the depth of the hole by inserting the screw into the countersunk hole, head first.
Drill a pilot hole for the screw into the centre of the countersink hole. Use a drill bit for the pilot hole no larger than 1/4 the size of the diameter of the screw. For example, if you are working with a 1/2-inch screw, use a 1/8-inch bit for the pilot hole.
Install the screw into the hole in the dowel with the screwdriver, until the head of the screw contacts the bottom of the countersink hole.
Push wood filler into the hole with your finger. Use enough filler to fill the hole to just above the surface of the dowel.
Allow the wood filler to dry. As filler drying times can vary between product type and manufacturer, carefully follow the wood filler's manufacturer's instructions. If in doubt allow the filler to dry for 24 hours. Sand the dried filler flush with the surface of the dowel. Paint or stain as desired.
If you are planning to stain the dowel choose a wood filler product recommend for use with stain.