Remove the doors and hardware, like hinges and doorknobs, from the cabinets.
Take the cupboard and doors to a garage or other workspace that is well ventilated. Place them on a drop cloth.
Spread a thick coat of paint stripper onto the wood using a stiff bristle brush. Allow the stripper to react with the paint for the time specified in the instructions.
Scrape the paint off with a putty knife or scraper, using a toothbrush in corners, smaller areas and on any intricate patterns in the woodwork. When scraping the paint, do not dig into the wood.
Scrub the wood with a cleanser that has a mineral spirit base.
Paint the bare wood with a coat of primer. Paint with the grain of the wood, covering 3 to 4 inches of the surface at a time with long brushstrokes. Keep an eye on the corners, because the paint can run down the sides and drip from there. Wipe up any drips with the paint brush. Allow the primer to dry.
Touch up any spots with primer where needed and allow it to dry.
Paint the cupboard doors with the top coat of paint, using the same method you applied primer with, and allow it to dry.
Move the cupboard back into the kitchen.
Reinstall the doors and hardware.