Sweep the floor with a broom and dustpan to remove all dirt and debris.

Attach a natural hair sanding pad to a floor buffer. Plug in the electrical cord.

Sprinkle 1/2 cup of polishing powder over a 4-foot by 4-foot area of the travertine tile. Drizzle 1 cup of water over the polishing powder.

Run the floor buffer over the travertine tile until the polishing powder and water turn milky white. Add more powder or water, as needed, to create a gritty solution on the tile surface. Repeat Steps 3 and 4 to polish the entire travertine tile surface.

Wipe the tiles by hand, using clean cloths, to remove the water and polishing powder. Follow by wet mopping the surface with a mop and bucket of water to remove any remaining powder residue. Dry the travertine tiles with clean cloths.

Secure a floor buffing pad to the floor buffer. Buff the floor again, this time using only the dry buffing pad. Allow the travertine tile to remain untouched for 24 hours.

Tape off floor boards and edges with painter's masking tape. Spray natural stone sealant over the travertine tiles in even, sweeping motions. Apply one thin coat at a time. Allow each coat to air dry completely before adding another one. Once you've achieved your ideal level of shine, allow the travertine tiles to dry for a minimum of 24 hours before walking on them.