Sand or scratch off the name and information from the front of the headstone. You do not want to desecrate the memory of the deceased by leaving his information and epitaph on the headstone while you are destroying it. You can use a hammer and chisel or an electric sander to obliterate the information.
Contact a local recycling center. Though not all recycling centers will take headstones, they will at least know where you can take the headstone. A recycling center will also know the best ways to get rid of an old headstone.
Contact a local headstone maker. Sometimes, the makers of headstones will purchase or accept used headstones to be recycled. If the stone is just faded, the headstone maker might be able to re-engrave it. If there is no headstone maker near you, look in the yellow pages to see where the nearest one is.
Contact your local garbage dump or sanitation service. The simplest way to get rid of an old headstone is to simply put it in the garbage. However, depending on where you live, your local garbage service may not accept such heavy objects in the normal trash. So you will have to get it approved.
Contact a local rock quarry if your local sanitation service does not accept the headstone. Some rock quarries will take old headstones and add them into their mined rock. However, this will depend on what kind of rock the headstone is made from. The quarry may be willing to help you identify the stone.
Break up the headstone with a sledge hammer if you cannot find any other way to dispose of it. The chunks of the headstone can be used in graveling or decorative landscaping. If nothing else, the chunks of the headstone will be small enough to be accepted in the trash.