Sand the entire surface of a pressed-wood bookcase using medium-grain sandpaper. Use small, circular motions with the sandpaper. This will remove any peeling, chipping or splintering or large areas of roughness.
Sand the entire surface of the bookcase using fine-grain sandpaper with the same small, circular motions as before. This will make the surface of the pressed wood smooth and even.
Run a vacuum with a brush attachment over the bookcase to remove sawdust and debris. Focus on the corners and creases to remove all of the debris.
Wipe the entire bookcase down using a damp cloth, then let the bookcase air dry for 30 minutes.
Fill the bottom of a paint tray with latex paint, then apply the paint in a thin layer over the entire surface of the bookcase using a 2-inch flat paintbrush. Allow the paint to dry for 4 hours.
Apply two more thin coats of latex paint, allowing the paint to dry for 4 hours in between each coat.
Apply a layer of clear latex varnish; an extra coat makes the covering more durable, just allow the varnish to dry for 4 hours in between coats.