Fill your kitchen sink with about 2 quarts hot water and 1 tablespoon dish soap.
Dip a cleaning rag into the soapy water, wring out and wipe it over the limestone to remove buildup.
Rinse out the cleaning rag, wipe down the limestone again with the damp rag and dry with a clean rag held in the other hand. Drying quickly prevents streaking and spots from settling on the smooth limestone surface.
Remove heavier buildup by spraying the limestone with a stone cleaner safe for this type of stone. Again, wipe off with a damp rag and dry with a clean rag.