Combine the cornmeal, water, and salt in a saucepan and bring to a boil. Once boiling, reduce the heat to a simmer and stir to remove any lumps.
Simmer for 25-30 minutes, stirring regularly to prevent the cornmeal from burning and sticking on the bottom, until the mixture has thickened and the there are no hard pieces of cornmeal left when tasted.
Serve immediately—or, allow to chill before cooling completely in the refrigerator. Turn out the set polenta, slice, and serve cold—or brush with melted butter and brown the slices under the broiler.