The best way to clean clams and mussels (especially the latter, as they are the briniest of all mollusks) is to fill the kitchen sink with cold water and approximately a teaspoon of sea salt.
Let the mollusks soak for ten minutes or so, then drain and fill the sink with clean cold water. Pull the "beards" from the mussels and use a vegetable brush to scrub away any excess sand.
Place the mollusks in a large strainer and run yet more cold water over them. Now they are ready to be cooked.