Fresh and healthy mussels should have a glistening shell and have no strong fishy smell.
If possible, get the fishmongers to place the mussels in ice and once at home, store them in the fridge until ready to use. Ideally you want to cook the mussels as soon as you can after purchasing to retain their freshness.
Discard any open (dead), cracked or chipped mussels. You only want to have mussels in tightly closed shells as these are alive. If any mussels are open, they best way to see if they are alive is to lightly tap on the shell. If it closes then it’s obviously alive (and thus, okay to use).
One by one, pick up the mussels and remove the beard (the hairy bits) by pulling down and towards the corner of the shell. They should come off easily with a good outwards yank. Try not to damage the shells or mussels within when removing the beards.
In order to ensure that you do not transfer any expelled sand and impurities back into the mussels, remove them by hand from the bowl of water and under a tap of cold running water, gently scrub off any remaining debris from the shells.