Storage is the key factor in maintaining the taste and quality of your fresh fish. Temperature and time are the two factors you need to consider.
The first thing you want to do is remove any wrapping the fish was bought in. Make sure you have a clean surface to work on. Wash your fish in cool or cold water and pat it dry. Re-wrap in wax paper and place in a container with an airtight lid. Shellfish can be kept in an airtight plastic bag.
Put your fish immediately in the refrigerator. The ideal temperature is 34-36 degrees F or 1-2 degrees C for most fish. Any shellfish can be stored up to 40 degrees.
Fresh fish will only last in the refrigerator for one or two days, and shellfish will last up to three days. For longer periods of storage, you must freeze the fish or it will spoil. However, do not refreeze the fish once you have thawed it.
There is a salt ice mixture you can use to super chill your fish, which will extend the storage life of the fish to up to seven days. Instead of storing it just on ice, store it in layers of salt and ice at 28 degrees, a lower temperature than normal fish storage recommendations. This will keep your fish fresh longer.
Fresh fish should smell briney like the ocean, not fishy. Smell your fish before you buy it if it is actual fresh fish and not sealed or wrapped. If it has a very strong fishy odor, chances are it isn't fresh.