Pick up the plywood door and place it flat on two sawhorses. Protect the floor underneath the sawhorses with a drop cloth.
Smooth the plywood surface with fine-grit sanding paper. On new plywood doors that claim to come pre-sanded, run your fingers over the surface to find any rough spots left by the manufacture and sand them with even, circular motions. For older doors, inspect the surface for any dings and sand them flush with the surface in the same way. Flip the door over and repeat on the other side. Inspect the edges of the door for any rough spots or splinters.
Wipe both faces and all the edges of the door with a tack cloth to remove any and all wood dust that was generated during the sanding process.
Brush a coat of wood primer on one face of the door and on the edges. Apply the primer by using long, even strokes of the brush that run in the same direction as the grain of the plywood. When the primer is completely dry--read the packaging for appropriate drying times--flip the door over and prime the other side in the same way.
Sand down the surfaces of the door after the primer coat dries--primer may raise the wood grains slightly, resulting in a rough feel. Don't sand the primer coat off completely, just buff the surface lightly with 400-grit sanding paper to knock off any high spots.
Brush on a thin coat of wood paint or wood enamel to the side of the door facing up, as well as the edges. Use enough paint to cover the wood evenly, but not so much that the paint runs. Apply multiple thin coats of paint instead of one thick coat to achieve complete coverage. Allow to dry completely.
Flip over the door and repeat Step 6.