Summarize:

Anywhere besides a formal dinner, it is acceptable to pick up the shell and fill it with a little bit of the broth and then suck the mussel and broth directly from the shell, although you may still want to loosen it with a fork first. When your mussels arrive, there will likely be a small amount of meat juice inside the shell, which can be quite enjoyable. Sucking your mussel from the shell allows you to easily enjoy the juices. While not generally considered polite in American fine dining restaurants, in other countries, like France, it is commonplace to use your empty mussel shell as a tool to pry out subsequent meat from the other shells. Use one half as a spoon and insert it into your next mussel to scoop out the meat. Grip the back of your first discarded shell with the open side facing out. Use your fingers to gently apply pressure to the top and bottom of the shell. This way, you can open and close the shell with your fingers and use it to pick up other shells. While this is often considered unusual, it is acceptable in most places to pry out all of your mussels at the beginning of your meal and enjoy them all at once. Particularly if your mussels come in a booth or soup, this may provide ease in eating.
Eat straight from the shell. Break your first shell in half and use it as a spoon. Use your empty shell as tweezers. Remove all your muscle from the shell before eating any of them.