The best way to clean kitchen cabinets with stuck-on grease and grime is to make a mixture of warm water, a small amount of white vinegar, and a splash of Dawn dish soap. Then spray that mixture onto the cabinet surface, give it a minute to break down the filth, then wipe it away with a clean cloth. For really tough stains, make a paste with baking soda and a small amount of water. Apply that to the problem area and begin gently rubbing it in with a cloth - take care not to use too much pressure or vigor and end up damaging the cabinets.