Cleaning a decorative concrete floor promptly when the floor finish has become dirty, marred, or lost its luster, and dust mopping no longer helps, will restore the initial gloss and preserve the integrity of the remaining floor finish. You should use a pH neutral cleaner, diluted in cool water, according the manufacturer’s instructions. Most neutral cleaning products do not require rinsing except when recoating with new floor finish because they do not contain strong acidic or alkaline additives. The best source of a good cleaning product is a local janitorial supply house. They'll also have the best prices. We use and recommend Spartan's Damp Mop Cleaner.
When mopping, be sure to keep the cleaning solution from getting too dirty, and do not allow the cleaner to puddle. You may want to use separate buckets for the cleaning solution, and to periodically rinse the mop. Also, do not use Swiffer Wet-Jets, bleach, ammonia, Pine Sol, or any harsh detergents. They will break down and discolor the existing floor finish, and maybe the concrete sealer as well ,which could then require stripping and re-application.
The ideal mop to use for damp mopping is a "loop end wet mop" made of a cotton/rayon blend or microfiber. Loop end mops are absorbent, re-usable, contact the floor surface continuously, and don't leave lint or fiber behind. Microfiber flat mops also work well. Tough marks that do not come up with a mop can be removed with fine steel wool or a light scouring pad.