We have found some good resources to tell you how to clean your wooden cabinets whether they are stained or painted. Below is some of their advice. Note that there are also some great store bought cleaners out there for wooden cabinets such as Pledge and the like.
General-purpose oil-soap wood cleaners work well for general care. Whatever the sealant, frequently clean and polish or wax your wood cabinets. Heat and temperature changes can dry wood. Wipe cabinets dry. Do not get wood excessively wet. Occasionally disinfect all surfaces with a diluted antibacterial cleaner without bleach. Wipe on, then rinse with a clean, damp cloth. Dry with a third cloth. Work with the grain of the wood when cleaning and polishing.
Wash painted cabinets with warm water and diluted all-purpose cleaner, wood cleaner, or white vinegar. Do not get the wood excessively wet. Rinse the surface with a second cloth and clean water.
Wipe areas that might be contaminated with food-borne bacteria with an antibacterial kitchen cleaner or a solution of 1 tablespoon bleach to 1 quart water.
If grease builds up, wipe the cabinets with ammonia and water. Rinse with clear water. For stubborn stains, loosen dirt with a paste of baking soda and water. Don't use abrasive cleaners or scouring pads because they can scratch the surface.