Clean your cabinets with a standard kitchen degreaser or all-purpose cleaner and allow them to dry. Sand the surface of the cabinets with 220-grit sandpaper. Run the sandpaper evenly over the surface area of all the cabinets, but don't go overboard.
Wipe the cabinets down with a feather duster or a rag. Apply one coat of primer that is specifically for cabinets made out of particle board or plywood with veneer. Allow the primer to dry.
Add one coat of paint specifically for cabinets made out of particle board or plywood with veneer. Run the paintbrush in one direction until the surface of each cabinet is evenly covered. Allow it to dry and repeat with a second coat.