Only eat in winter, and always ask locals if they eat 'em.
In British waters, there is something called a red tide.
I'll explain. Mussels are filter feeders. When the water gets warm, a reddish type of algae in them. These can actually kill you, and no cooking will help. Chances are they won't be there in winter.
Here in Zeeland, we also have an old addage, that you must only eat the shelfish in the months with an 'R'. So not in May, June, Juli, August. This is a good rule of thumb, because the shellfish are reproducing in these months, causing them to be soft, white, and not very tasty.
As for cooking them, once you are completely sure that it's safe, you just stick your knife in the oyster, at the rear hinge. Then cut right through the closing muscle. (Nothing beats a fresh, salt raw oyster straight from the shell
) Mussels you can just lie on the ground, find a heap of grass and light over it. You can do this with the oysters too. Also watch RM aboriginal britain, he cooks some seafood there to. Don't eat the mussels raw though.
I'm yet too meet a non zeeuw (person from zeeland) who likes eating raw oysters
but we love them.