How to Pick Fish Select the freshest fish available. Look for fish with bulging, not sunken, eyes, and a sweet fresh smell (shark and skates, exceptions to the rule, will actually have a slightly ammoniated smell when very fresh). Store fresh fish in the coldest part of the refrigerator, even wrapping in plastic wrap and placing on ice chips if necessary. Lean fish keeps longer than fatty fish, but in no case should you keep it longer than two days. Freeze fish immediately to keep it longer. Do not freeze fish that has already been frozen.