I wash with hot water, a bit of detergent, a color catcher on a light cycle. I'll pop it in the dryer if it's real damp. Otherwise, it dries as I iron it, fold it then store with the rest of the stash.
Anything smaller than a FQ (some shops I get scraps from) I soak in a tub with a bit of soap, rinse and lay on a towel before ironing. Other times, I just sort and throw the scraps in with the rest. Just depends on time and if I'm doing other fabrics then too.