Best Storage:
Fridge
Cut celery into sections and place into a paper-towel-lined storage container or wrap in a beeswax wrapper in the fridge. If your celery is going soft, put it in some cold water in your fridge to crisp up again.
Freezer?
Yes
Chop and blanch for 2-3 minutes. Cool in ice water. Dry and freeze in an airtight container.
Use it up!
Freezing celery will destroy the its crispness, however once defrosted it can be used in soups, stews and other hot dishes where crunch is not necessary.
Use it all up! Keep the leaves to make a vegetable stock and re-sprout the root end to grow more free celery!