The first step is an assessment of the extent of the damage. If you notice scratches, it may be time to take your marble flooring to a professional for full restoration. You can try to polish the surface by yourself but if scars are too deep or wide-spread, polishing might just make them more visible. On the other hand, you can try to go for marble polishing, which is often just about removing dirt and light scratches. If your flooring is not severely damaged, you may be able to save the shine of your marble flooring with a thorough polishing.