Cleaning your Shellfish:

Before mussels and clams are cooked, the shells must be scrubbed in cold water with a stiff brush to remove any barnacles and sand. Reduce the amount of interior sand by soaking them in cold water mixed with a few handfuls of cornmeal for 30 to 60 minutes. 

Debearding the Mussel

Wild mussels (mussels are also farmed) require an additional cleaning step -- debearding. Protruding between mussels' shells is a small bristle or beard, by which the mussel attaches itself to rocks or pilings.  Shortly before cooking, remove the beard by tightly grasping the hairs near their base and giving a sharp tug. The beard should snap off along with a tiny bit of mussel flesh.