Shirley...this topic was posted here a couple weeks ago.
As a hardwood floor installer, I recommend a damp (never wet) towel / mop. Steaming is bad...oil soaps are bad. For stubborn area I use a swiffer type pad. The trick is go as dry as possible and use minimal amounts of cleaner.
Keep in mind its normally not the "wood" you are cleaning but the "poly finish" that has been applied to it. Water type product should NEVER be used on "non coated" wood...
You would not mop a fine wood dining table would you?
luke warm vinegar water.
I use white vinegar on a mop that is wrung out, not really wet.