Wrap the fudge in wax paper, cover it in aluminum foil, and then store it in an airtight container. The wax paper will let your fudge breathe and keep it from sticking.
If you wish to eat the fudge within a week, you can store it on the counter or in the pantry, but to preserve its flavor and texture for a month or two, store it in the freezer.
Even if your fudge has mix-ins like nuts, cookie bits, or a caramel drizzle, the freezer will keep it fresh. Storing fudge in the fridge, however, will cause it to dry out fast.