Personally, I like to hang my hair falls, rather than lay them flat. I find there is less chance of anything getting crushed (if there are feathers or more "delicate" trims) as well, if they are hanging there is less chance of them getting tangled up.
The only negative of hanging the falls is that over time the elastic at the top will more than likely stretch and get rather looooonnnngggg . . . ;)
All the hair falls are designed with the actual cording* being looped at the top. If you ever need to replace an elastic (either you want to change the colour to better match your hair colour, or it has stretched out) gently unloop the existing elastic. Before you pull it out, loop the new, fresh elastic onto the old one. This way you can be sure you pull it through the entire loop of the falls and don't miss any of them.
(*I'm calling the string or material the shells/accessories are braided onto "cording" for lack of a better word. This actual material varies between the different sets of hair falls I've made)