Limestone is a porous stone, prone to absorb stains quite quickly. If your limestone is outdoors and exposed to the elements, it is especially likely to become dirty. While sealing limestone does not make it stain-resistant, it does buy you some time to wipe up dirt before the stone becomes tarnished. Seal your limestone immediately after installation and then again about once a year.
Mop the limestone with a neutral cleaner -- if your limestone is particularly dirty, use an alkaline stone cleaner. Let the cleaner sit on the limestone flooring for at least 10 minutes and then scrub the floor with a deck brush. Rinse the floor with clean water and let it dry completely.
Apply an impregnating sealer to the stones using a soft cloth, such as lambswool. Do not let the sealer puddle. Allow the sealer to dry per the manufacturer's instructions.
Apply a second coat of sealer with a soft cloth.
Buff the limestone after the second coat dries using a microfiber or cotton cloth.
Never use cleaners that contain bleach, acid or alkaline on limestone. Don't walk on the limestone until it is completely dry to the touch.