Remove all hardware, Mark doors and drawers to know where they go back. Wash down with TSP and then sand off sheen. Prime with oil based primer, lightly sand smooth, then paint with oil based paint.
Clean with TSP - it works wonders for that task .. follow directions exactly!
How to Paint Cabinets
Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 100 grit sandpaper or a green Scotch Brite pad.. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like KILZ. Acrylic or water base paints are low-fume and clean up easily with water. Alkyd or oil-based paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.