How can I get built-up old grease off of wooden kitchen cabinets?

A good friend of mine just got a divorce, and moved back into the house that she owned with her husband. When she left him, he remained in the house, not maintaining it or cleaning it. Now that she is back in, she wants to get the house in order. It’s in such bad condition it’s kind of depressing.

I figured to try to help her in one little affordable way, I would try to paint her kitchen cabinets, since she can’t afford new ones right now. The problem is, the cabinets have old heavy duty grease on them. Once I get the grease off, I can remove the hardware and paint them.

How can I clean the old, heavy duty grease off the wood kitchen cabinets to prepare them for painting?