Limestone is a carbonate, sedimentary rock that has been used in the construction of some of the world's oldest monuments (e.g. the Roman Colosseum and the Pyramids at Giza). In nature, limestone can be found anywhere water has flowed, even in caves where it can take the form of stalagmites and stalactites.
Dish soap and a soft cloth will ensure the stone is properly cleaned, and won't scratch the stone as a result of any heavy scrubbing. In general, acidic and harsh cleaners should be avoided as they can cause damage. Having your limestone properly sealed will also help avoid any damage to the stone, and it is recommended to reseal it once a year if it experiences regular use.
Limestone can be scorched, so potholders or trivets should be used under hot cookware. For heavy stains, a mixture of peroxide and flour can lift a stain over time, but preventative care is the best kind of care.