Take the doors off the cabinets by removing the hinges, using a screwdriver. Take the handles off the doors with the screwdriver once the doors are removed.
Clean the cabinets, using a kitchen cleaner and a rag to remove all food and grease. Grease makes sanding off cabinet paint more difficult. Let the cabinets dry.
Place a drop cloth on the floor underneath your sanding area, and sand the paint off all the doors and the cabinets, using 150-grit sandpaper. Use a belt sander to make the process a bit quicker.
Wipe the surfaces of the cabinets with a dry cloth to remove the sanding particles.
Apply a primer to the cabinets, using a primer paintbrush. Use a high-quality primer to prevent peeling of the paint. Allow the primer to dry according to the manufacturer's instructions.
Apply paint to the cabinets, using a brush appropriate for the type of paint you selected. Oil-based paint tends to be the longest-lasting, so use that and an oil brush. Allow the paint to dry.
Reattach all the cabinet hardware.