Depending on what kind you have (Organza or netting), your mileage may vary on storage. I'm going to be using a true vintage organza chiffon petti as my example.
One thing I find handy is storing the petti in a bag that is the same color as the petti itself. That way when I grab the pink bag, I know I have the pink petti.
If you're not a sewer, the same effect can be had with a pillowcase. I happen to have a ton of fabric, so I've decided to make my own.
You never want to hang vintage petticoats on a hanger for long periods of time. the weight of the fluffs will pull down over time and flatten them, plus hanger clips can snag waistbands.
With the drawstring bag you can either tighten the string and hang it on a hook, or clip the top of the bag to hanger clips and hang it up
It takes about 15 minutes if that. Sorry this post is kind of short. I'm coming down with the flu :(