Unscrew all of the cabinet hardware, hinges and knobs with a screwdriver. Lay a drop cloth on the counter tops or a work surface. Set the cabinet doors on the drop cloth.
Pour 1/3-cup all purpose cleaner and 1 gallon of water into a bucket. Dip a sponge into the mixture and wipe down the cabinets.
Attach a piece of 100-grit sandpaper to the bottom of an electric sander. Run the sander over the surface area of the cabinets. Repeat with 220- then 320-grit sandpaper. Run a tack cloth across the surface of the cabinets to remove any sanding residue.
Dip a 3-inch nylon paintbrush in oil-based primer and cover the cabinets with a light coat. Give the primer four to five hours to dry. Use your paintbrush to apply oil-based paint onto the cabinets in a light coat. Allow the cabinets to dry overnight then cover them with another light coat, allowing for the same amount of drying time.
Dip the paintbrush into oil-based varnish and cover the cabinets with a clear coat. This will protect all of the hard work you've done. Give it 24 hours to dry.
Use your screwdriver to reinstall all of the cabinet hardware, hinges and knobs or replace them with new components.