Create a mixture of oxygen bleach and hot water. Many chemicals and acids react with limestone to the point of causing the stone to etch or dissolve, but oxygen bleach is natural and safe. Since not all oxygen bleach manufacturers use the same concentration of ingredients, read the label carefully to determine how much water you must use.
Dampen a cloth or sponge with the oxygen bleach solution. Use a cloth or sponge that's soft and non-abrasive because, as a natural stone, limestone can scratch easily. Wring out your cloth or sponge to remove the excess moisture, since limestone is porous and can trap moisture if you saturate the surface.
Scrub the entire limestone countertop with your sponge or cloth. The oxygen bleach solution should break down any set-in stains while also restoring the natural shine to the limestone surface. For added effectiveness, leave the bleach solution on the countertop surface for 15 minutes or more, because oxygen bleach products work by gradually releasing oxygen ions, a process that does not happen immediately.
Wipe down your entire limestone countertop with a second cloth or sponge. This second cloth should be mildly dampened with water to rinse the oxygen bleach solution from the surface. If any stains remain, or if the limestone still does not shine as well as it could, scrub with oxygen bleach a second time and then rinse again.
Wipe the countertop with a towel to dry the moisture. Water spots can appear very prominently on the bright and smooth surface, if mineral deposits form. By drying the limestone by hand, you can prevent these mineral deposits from appearing.