Summarize:

Spray the cloth with water. Afterward, add a few drops of an appropriate cleaning solution to the floor. Gently rub the stained area, taking care not to apply too much pressure as scrubbing or rubbing the floor aggressively will harm the finish and the wood. Any stains that are set in need to be buffed out and the finish has to be reapplied.  Remove shoe scuffs as soon as possible. Never use an oil-based cleaner—it will leave your floor cloudy and streaked. If you don't have cleaning solution, apply a small 1 inch (2.5 cm) drop of real mayonnaise and let it sit for 15 minutes. Afterward, wipe it off using a soft, damp rag. In many cases, the mayonnaise will remove the stains. Move in strips 10 feet (3.0 m) in length. Always begin with the baseboards and move outwards, taking care to overlap each band by 2 to 4 inches (5.1 to 10.2 cm). When moving toward the entrance, move backward at about 1 to 2 feet (0.30 to 0.61 m) per second, moving the buffer side to side slightly as you move.  Always check with the manufacturer regarding bamboo floor care and refinishing to make sure your buffer can be used to clean it. Do not wax the bamboo or use oil cleaners. If you wear shoes on your bamboo floors, you might end up with a scuff here or there. Dilute the wood floor cleaner with water as required by manufacturer instructions. Dip a soft rag into the mixture and firmly scrub in circular motions over the scuff marks. Dry the spot with a rag when done.  Be sure that your cleaner is indicated for use with bamboo flooring. Use a high-absorbency microfiber cloth to dry to area. Never use an oil soap, even if it says you can use it on a wood or bamboo floor. Similarly, don't use a wood cleaner that contains a wax. These products can cause a waxy buildup. Don't use an abrasive rag or product to scrub the bamboo floor, as this can damage it. It may take longer to remove the scuff marks with a soft cloth, but it will reduce the likelihood of damage.
Remove stains with a damp cloth and cleaning solution. Buff the bamboo flooring with a buff sander to restore its luster. Remove shoe scuffs immediately using wood floor cleaner and a rag.