Murphys' oil soap and water
Get a good brand of cleaner for hardwood floors and follow the directions on the bottle. We bought a rug doctor machine that has heads for carpet and one for hard floors. You use an all purpose cleaner made for the floors, it puts down the liquid, then sucks up the dirty liquid into a different tank and the floor dries in seconds, leaving a clean, shiny floor behind. It soaks the water up enough that you could even use it on laminate floors. It is no bigger than a normal upright vacuum cleaner. Not real cheap, but it really does the job!
Sweep or vacuum first - are they old fashioned formerly waxed? if so, try vinegar & water mixed 1 part vinegar to 2 parts water - or Murphy's Oil soap. Barely damp mop. If they have polyurethane Ace Hardware has appropriate cleaners.