Drill pilot holes slightly smaller than the screws into the two pieces of wood. Pilot holes are holes smaller than the screw that help guide the screw in place so it doesn't twist off center.
Place the pieces of wood together. Line up the pilot holes. If both pieces are movable, clamp the larger of the two pieces to a workbench to provide stability while driving the screws into the joint.
Insert the screw tip into the top pilot hole and screw through the first piece into the second piece of wood. Sink the head of the screw below the wood surface.
Measure the diameter of the hole. Buy a wood dowel or ready-made wood plugs in the same diameter size. For wood dowels, slice a circle off the end to make your own wood plug.
Coat the screw head liberally with wood glue and place the plug into the hole. If the fit is too tight, sand the diameter down.