Determine if there is a clear sealer over the stain on the door, and how long the door has been stained. When the door does not have a clear sealant over the stain and the stain is less than two weeks old, wait until the stain has had time to completely cure to paint.
Sand the door with 200- to 400-grit sandpaper once the stain has cured, or if the stain is older, or protected by a clear finish. Sand the entire surface lightly, while sanding the edges a little more aggressively.
If the door has carved details, take a wire brush and try and rub it over any irregular surfaces.
Wipe the entire surface with a tack cloth. Do not use any kind of cleanser or chemicals, as this may keep the primer from adhering to the surface.
Tape off any hardware on the door to avoid getting paint on it.
Apply a thin coat of an oil-based primer with a paintbrush. Water based primers may not adhere to this type of surface to provide a long lasting bond.
Allow the primer to dry -- about two hours, or whatever is recommended by the manufacturer. Lightly sand the entire surface again with 400-grit sanding paper. Clean with a tack cloth.
Apply a second coat of primer and let it dry.
Apply your choice of paint over the primer. Use a roller on larger spaces and a small, angled brush on on panels and details. Let dry and apply another coat if necessary.