Is there liquid on the meat? If so, that liquid should be clear, not milky. Milky liquid on a fillet is the first stage of rot. If the fishmonger lets you, press the meat with your finger. It should be resilient enough so your indentation disappears. If your fingerprint remains, move on.
Shellfish
Buy only at the finest fish markets. These are the places where turnover is so rapid you can be assured of fresh mussels, clams or oysters. You may still get a dead one, but the ratio will be far lower.
What is a dead one? Shellfish are sold alive, so they should react to you. Put them on the countertop and back away for a moment. Then tap the shell: It should close tighter than it was. Oysters are a little tough to do this with, but clams and mussels will definitely react. You can also tell a dead shellfish after you’ve cooked them all. Dead ones do not open after being cooked. Throw them away.
Scallops are a special case. Scallops are almost always sold shucked, so what you are looking for are “dry packed” scallops, meaning they are not shipped and stored in brine. Those scallops you see wallowing in milky ick? Leave them be. Better to buy frozen, vacuum-sealed scallops, which are perfectly good by the way, than an inferior wet-packed scallop.
Prawn & Shrimp are easy. Buy them whole and frozen. Whole because the shell protects them from the rigors of being frozen without losing too much moisture, and frozen because prawn & shrimp cook (and rot) very rapidly.
Should you be near a prawn or shrimping region or have access to truly magnificent fresh prawn or shrimp, by all means, buy them with the head on if possible. Why? Because head-on prawn and shrimp stay moister. Remember: Nothing says boring like a dry, overcooked prawn or shrimp.
All the information about prawn and shrimp applies to crayfish, too. Unless you can get them live, in which case, follow the instructions for lobsters or crabs.
Squid or octopus are almost always sold to the wholesaler pre-frozen, so you should buy them frozen. Both squid, commonly known as calamari and its more richly flavored cousin the octopus, freeze exceptionally well. Again, if you can buy squid and octopus not to mention cuttlefish fresh, do it! They are rare treats even at fine fish markets and should be appreciated as such. Like finfish, you should look first at their eyes, which should be clean and bright.