This is a pretty traditional preparation of mussels; steamed in white wine, shallot, and garlic. In this case I added tomatoes, which may or may not qualify this as moules marinieres depending on who you ask. This is pretty much a template recipe with infinite potential variation on flavors. If you like anis, substituting pastis or similar (ouzo, arrack, etc) for the white wine is very tasty.
Your mussels must be clean, de-bearded, and alive. The best way to get beards off is a to do a twisting pull with a pair of pliers (demonstrated at about 4:45 in this video by Lil's favorite, Alton Brown). Definitely at no point should they be placed in water; this will kill them, and dead shellfish become poisonous very quickly. You can briefly rinse them in a colander however. Perfect cleanliness is neither possible nor essential, and being overly fastidious will likely just kill them.
Let them sit out for half an hour or so before prep, so that the live ones close up tight. Sort through for any that are hanging open, and flap them open and shut; if they're alive they'll shut themselves in response. Toss any that don't respond.
3-4 shallots - peeled and chopped coarsely
5-6 cloves garlic - peeled crushed and chopped coarsely
~1 cup white wine
Lots of butter
Optional extras: tomatoes canned or fresh, lemon juice/zest, herbs, etc
You need a pot with a good lid and lots of space for the mussels to steam. A wok is perfect. Don't overdo it on the liquid, as the mussels release plenty of their own.
Sweat the veggies etc in butter with a bit of salt. Toss all the mussels in, add the white wine, and clamp the lid down. After about 2 minutes, toss them to make sure they're steaming evenly. Steam until they're all open, which shouldn't take more than another 2 minutes, after which time you're in danger of overcooking them.
For service: I like to just plop them on top of a bowl of spaghetti. Be generous with the sauce, and make sure you've got some crusty bread to sop up the extra. Moules frites is a popular standard in France, where you usually get 1kg of mussels and unlimited fries for around 10E, so keep an eye out for that sign if you're ever looking for a damned tasty meal which is affordable by French standards, and can't really be messed up.