Clean the terrazzo floor with a wax-stripping product that's safe for terrazzo. Follow the directions for removing wax. Wash the floor well with water to remove all traces of the wax-stripper. Let the floor dry completely.
Seal the terrazzo floor with a sealer. This protects the cement from most stains. Apply the sealer according to the package directions and let it dry well. Usually one thin coat is all the floor needs.
Keep dust off the floor. Because dirt is abrasive, it can scratch the surface of the sealer, so you need to regularly sweep the floor either with a vacuum, broom or dust mop.
Use a neutral pH floor cleaner or one made especially for terrazzo floors. Mix 1 cup cleaner to 3 gallons of water or whatever the manufacturer recommends. Apply the cleaner and let it set for a few minutes. Mop up the cleaner with clean water. Keep rinsing the floor until there are no mop lines.
Buff the floor if you have a buffing machine. If you don't have a buffer, skip this step.
Wipe up spills immediately. The longer a spill sets on the floor, the greater chance it has of permeating through the sealer and staining the terrazzo floor.