Break the cabinets down to as many pieces as possible. You don't have to completely dismantle the cabinets, just remove any hardware, such as knobs, pulls and hinges. Set the hardware aside and place the doors and drawers on a clear work space.
Spread a finish-stripping solvent over the surface of the wood. Mineral spirits work best for many finishes, but shellac and lacquer will respond better to denatured alcohol. Allow the solvent to soak into the peeling finish for about 10 minutes.
Scrub the old finish from the wood with a rag, scrub brush, paint scraper or 0000-grade steel wool. Apply more solvent as necessary and allow it to soak into the finish before attempting to scrub again.
Wash the wood with trisodium phosphate. Dilute the trisodium phosphate as directed on the packaging. Typically, you can mix between 1/4 and 1 cup into 1 gallon of hot water. Read the label on the packaging for specific information.
Rinse the wood with a damp rag and allow it to dry completely. Mix stain as directed. Paint the stain onto the wood with a rag or a paintbrush. Dip the rag or brush in the stain and wipe it against the lip of the can to remove the excess. Spread the stain with the grain of the wood and wipe the wood with a dry rag to soak up excess stain. Allow the stain to dry.
Mix and apply protective sealer as directed by the manufacturer. Mixing, application and drying all vary by product and manufacturer, so read the label thoroughly before using the product.