Remove hardware, doors, and drawers. Put pieces of painter's tape on each hardware item, door, and cabinet interior, and label them with the same number so it's easy to put them back where they belong.
Apply degreasing cleaner to boxes, shelves, and doors, following manufacturer instructions. Wipe thoroughly. Let dry for at least a day, to avoid any moisture bleed-through in the final finish.
Sand boxes and doors with 150-grit sandpaper or apply deglosser. Wipe with tack cloth. Using a microfiber roller, apply a thin coat of paint or primer (if your paint does not contain a primer); nip into narrow areas and details with brush. Let dry thoroughly. Lightly sand again and wipe clean.
Repeat using method above, applying multiple thin coats of paint. Let dry completely.