Put a strip of painter's tape on the wall. Make sure that it is placed right up against the door frame to keep paint off the wall.
Sand the woodwork on the door frame with 80-grit sandpaper or a sanding block. You don't need to entirely remove the glossy stain or wood sealer, but simply scuff the surface. Wipe off the door frame with a damp rag to remove any dust.
Apply a coat of shellac-based primer with a white china bristle brush. Work quickly, as the alcohol in the primer evaporates quickly. Do not brush over areas of paint that are beginning to dry or the primer may get gummy.
Clean shellac-based primer off your brush by rinsing it with denatured alcohol. Wipe excess alcohol from your bristles with a rag.
Lightly sand the door frame with 220-grit sandpaper. Run a damp rag over the sanded woodwork.
Brush on two coats of latex paint with an angled sash brush. Let the paint dry between coats. Remove the tape.