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Refinishing marble is simply a matter of abrading the surface with a power sanding machine, using progressively finer grits until the scratches in the marble are microscopic, causing the surface to become reflective.
I have never tried to refinish marble, so I am not about to offer you any hands-on personal advise, but I can refer you to a couple of websites and also a good book that have all the information you need...
Hardrock Stone Care Products, a company specializing in cleaning and refinishing products, have instructions for their products posted here: http://iptmanufacturing.com/site/data. These instructions are really "primers" on how to properly clean and restore marble and other natural stone. Cool!
Refinishing marble is not the typical do-it-yourself project, but I hope this infusion of inspirational material gets you started on the right path!