To polish marble tiles, apply a polish made for granite, and use a polishing machine to buff the tile. If the tile is damaged in any way, file it and remove any scratches before the polishing process to make the tile look smooth again.
Apply a quarter-sized amount of polish to the center of a polishing pad. Attach the pad to a 4-inch angle grinder, and pass the grinder over the surface of the tile in a circular motion. Do this until the pad dries, leaving the polish a light gray color on the tile. Once the polish dries, pass the pad over the area again until the polish becomes glossy. Repeat the process until the tile is as glossy as desired.
Use an orbital sander with 100-grit sandpaper to smooth any damaged tile. Apply the sander to the tile's surface in small circles. Pass over scratches and rough edges until the grooves are level with the rest of the tile. Replace the sandpaper with a 150-grit piece, and pass over the scratches and rough edges until they are no longer visible. Switch the sandpaper again for a 220-grit paper, and pass over the tile once more before applying the polish.