Label each cabinet door so you can put them back in the right place. Either draw a diagram showing where each door goes and label the door with a pencil or a piece of tape, or make a mark on each door and the corresponding cabinet it fits.
Remove the hinges and the door pulls. Tape the hinges and screws to the back of the cabinet with masking tape. Place the door pulls in a solution of detergent and water and let soak for at least an hour.
Lay the doors flat on a drop cloth.
Clean each cabinet with a strong detergent and warm water. Use an SOS pad (not Brillo) to scrub badly soiled spots.
Determine the type of finish on your cabinets. Shellac dissolves in denatured alcohol. Wax dissolves in turpentine. Polyurethane and varnish can be removed with paint or varnish stripper.
Use a commercial semi-paste or gel stripping product that's recommended for your finish. Follow the manufacturer's instructions.
Rinse the cabinets well with clean cloths and plain water. Use fresh cloths as needed. Let the cabinet doors dry well.
Use the same stripping method on the frames of the cabinets that you used on the doors. Use drop cloths to catch any spills. Don't let the stripper run down the surfaces. This could cause streaks.
Refinish, wax or paint the cabinets before you reinstall the doors. Scrub and polish the door pulls and reattach them.