Petticoats can be made of gathered chiffon, which tend to stay poofier longer, or layers of gathered tulle, which tend to deflate after a few wears and often need to be layered one on top the other to get the desired poof.
Petticoats should never be worn as a skirt and should also not be longer than the skirt they are being worn under. It's generally considered best for them to be a couple inches shorter than the skirt they are worn under for maximum effect.
Sweet Rococo sells a lot of petticoats as well as Bloomers. Another brand that sells a lot of quality petticoats and undergarments such as petticoats is Fanplusfriend Garden. Another popular brand that sells good quality petticoats with a lot of volume is Classical Puppets.