I second and third the Krud Kutter recommendation in Replies 21 and 36. Just spray it on the dirt and wipe with a white terry cloth rag; couldn't be easier. It will work on door handles, too. In fact, I wouldn't be surprised if it cleans the dirty area so well that you will need to clean the rest of the door that you think looks clean. Throw the rag in the washer and you're done lickety split. If you buy Krud Kutter at Home Depot, look for it in the paint department.