Determine what the tomb stone is made of. Limestone and sandstone were popular options for many years because they're easy to carve. These materials don't age well, however, and marble and granite became the stone of choice. More recently, bronze has become a more popular choice. Each material has distinctive properties that require a different method of protection. Granite and bronze will not be harmed by acid rain like marble, limestone and sandstone.
Clean the stone thoroughly using warm water and a soft brush. You can use a soft bristled toothbrush to remove mosses or lichens, and to clean in the carved letters. Be sure that the cleaner is non-ionic and non acidic. Dissolved baking soda is the safest choice. Avoid bleaches, detergents and abrasive cleaners.
Apply a penetrating sealer, like Endur-O-Seal with Teflon, or Aqua-Mix. These products were designed to protect concrete from acid rain and rust stains, and can also be used on limestone.
Plant a shrub for shade, or build a protective canopy over marble tomb stones. Researchers have been trying to develop a protective formula for marble, but since it isn't porous, progress has been slow.
Rinse the tombstone frequently with an alkaline (like baking soda). Rinse the stone after each rain to counteract the affects of any acidity.