Wet a cleaning rag under warm tap water. Wring it out and drizzle the rag with dish soap.
Wipe over the cabinets, starting at the top and wiping downward. Follow the grain of the wood.
Rinse out the cloth. Drizzle with fresh soap as needed until you get all the grease off the cabinets.
Rinse the cloth with plain water this time. Wring it out and wipe over the wood to wash off any leftover soap.
Apply a layer of oil soap to the cabinets if you wish to restore moisture and shine. Follow the instruction on the container, which often direct you to simply wipe a thin layer of the oil soap over the cabinets and either allow to air dry or wipe off with a damp rag.