Remove the cabinet doors and drawers. Loosen the screws on the hardware with either a flat-head or Phillips screwdriver, depending on which type of screws were used. Place the hardware in a safe location for later use.
Place a plastic tarp or drop cloth on a flat surface. Lay the cabinet doors on the work area. Pry off any loose paint with a putty knife. Clean the entire cabinet with trisodium phosphate and a damp cloth. Thoroughly rinse with warm water and dry with a cloth.
Sand all the surfaces of the cabinetry with 150-grit sandpaper and clamp it to a hand sander to make the process easier. Remove any dust with a vacuum hose.
Paint the insides of the doors with a roller, using an acrylic water-based primer. Roll paint on the drawer fronts and paint the fronts of the doors once the insides are dry, which should take about 2 hours. Once the paint is dry, sand all surfaces with a 220-wet-dry sandpaper and vacuum up any dust.
Roll on the satin enamel paint on top of the primer. Wait for it to dry and apply a second coat. If you are satisfied with the coverage after it dries, then you do not need to apply a third coat.
Reinstall the hardware with a hand drill and hang the cabinet drawers.