To store feta cheese properly, keep it unwrapped in an airtight container or wrap it tightly in plastic wrap or aluminum foil before moving it to the refrigerator. It is also possible to store it in brine in the fridge, but you must change the water daily.
Feta should not be frozen, as this will alter its texture and flavor. If you need to freeze feta, though, use it within a few months after defrosting and consume it immediately after thawing.