Your mussels are alive, and you want to keep them that way until cooking. Dead mussels deteriorate quickly and can make you very sick if you eat them. Luckily, dead mussels declare themselves by staying closed after cooking. Throw those duds away. The mussels that you have are 24 hours out of the water, so there should be very few dead bodies.
When you pick up your new bivalve friends, they will be packaged like this.
Mussels cannot be wrapped in plastic. EVER. They will die. So, inside the soft cooler you will find an ice pack, ice chips, and newspaper. The bundle of mussels will be wrapped in newspaper to protect the cooler from the mussels and the mussels from the air. Mussels are finicky, they hate direct contact with air but they can only be covered by breathable materials.
The bag of mussels inside will be fresh out of the water. There will be seaweed, grit, baby mussels, moss and maybe a worm or two. My strategy is to leave the mussels as-is until right before I cook them.
If you are not cooking the mussels immediately, place them in a bowl with ice and cover them with a wet rag or paper towels.
Keep the bowl in the coldest part of your refrigerator and change the ice out daily. When kept this way, the mussels should be good until Thursday or Friday.
I hope you enjoy eating these pretty little guys. Please see the recipe for Beer Steamed Mussels for instructions on how to clean and de-beard.