Mussels cook quickly, that means they'll overcook quickly, an overcooked mussel is tough and stringy. The easiest way to avoid this problem is by using as wide a pan as possible over very high heat. That will expose all the mussels to the hot surface of the pan so they cook together at the same speed. If you don't have a skillet that big, use two skillets but make sure its just one layer.
I recently discovered I like mussels. I had them at a restaurant and thought they were great. I was scared to try them before, maybe I'll cook them at home sometime soon.
I eat mussels every week.....put them in a large pot with about 4 inches of water with a tablespoon of salt ...cover and bring to a boil...as soon as it starts to boil ,time 10 minutes ...the mussels don't have to be covered with water.....I save some of the water and put a dallop of butter in it and rinse my mussels in them ....some good eating