Firstly, pick over the mussels and discard any open ones that refuse to spring closed when they’re lightly tapped; failure to do so means they’re dead and their freshness is in question, so definitely don't risk cooking the odd one or two in this category.
Secondly, discard any with broken shells as these too would certainly be questionable.
Fill the sink with cold water and one by one scrub the mussels, removing barnacles and tugging off the "beard".
You'll need to inspect mussels that are unusually heavy, as these are usually full of sand when you open them.
Rinse thoroughly several times before cooking as you really don't want a mouthful of grit or mud.
Don't leave live mussels standing too long in fresh water, or they will die and be useless.
Although they need a bit of work before you get to the cooking stage, mussels are ridiculously easy to cook.
Cooking mussels is easy. Add them as specified in a recipe to a pan of water, stock or wine – usually onions and/or garlic are softened in a little oil or butter first – then cover and bring the liquid back to a boil and allow to simmer for a minute or two. The mussels will cook in this short time, over-cooking should be avoided as it can lead to a rubbery texture. The mussels will open when they’re cooked, if you see a rogue one that refuses to open, simply remove it as you finish off the recipe.