Dirt, dust and grime can scratch hardwood floors and cause damage to the floor's finish. The most common cleaning instruments needed for hardwood floors are a vacuum and a dust mop. If your hardwood floors are very dirty and you can't use water to clean them, it limits your options for getting the floors very clean. It is possible, however, to get some of the dirt and grime off the floors without water.
Vacuum the hardwood floors well to get up as much dirt and dust as possible.
Wipe the floor with a soft dust mop that picks up pieces of dust. This will get any dust the vacuum missed.
Dab a quarter-sized drop of wood soap on the cloth and scrub the soiled places on the hardwood floors with the cloth to remove as much of the stains as you can.
Dampen a cloth with 1 tsp. vinegar and wipe down any stuck on grease on the hardwood floor.