This is what the floor looks like after using diamond pads.  It is dull because a layer of stone has been sanded away.  Some scratches will be removed in this step.  Diamond pads vary in roughness.  So, the rougher the pad, the more scratches that get removed.  Starting with a rougher pad will yield better results but adds to the amount of work required to finish the job.

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After using the diamond pads, polishing powders are required to make the floor really shine.  Sealing the tile is done after this step.

Once the tile sealer has dried a final buffing will be required.  This the same section of floor shown above.  The darker tiles will get shinier than the light tiles.

Make sure to use a neutral floor cleaner to take care of any stone.  Home Depot carries a line of products called Zep that will work.  Acidic products like vinegar will eat away the shine.  Aggressive detergents will remove the sealer.  Buy a swiffer and washable microfiber pads to help with floor cleaning.