Soggy, floppy celery is the worst. Here's a celery tip I once read in a newspaper column called Hints from Heloise, a housekeeping advice column. When you get fresh celery home from the grocery store, take it out of the little plastic sleeve, if they've put it in one at the store, and wrap it in aluminum foil, covering all explosed surfaces of the celery. Store it in the crisper drawer of the fridge wrapped in that foil. It'll keep the celery crisp for up to two weeks. I've tried this and it works great!

If you're going to use the celery within a day or two, another way to keep it crisp is to clean it and trim the leaf and root ends, then stand the trimmed stalks at least halfway immersed in a container of cold water in the refrigerator. That keeps it hydrated and cold, and it stays crisp. You do have to dry it off a bit after you get it back out of the water, but at least your celery won't have gone soggy on you.