I can't work in chaos, so I keep my work area pretty neat. I'm lucky to have lots of cabinets in my laundry room, so all my fabric goes there (the shelves are lined with acid-free paper). Small notions and thread go in my sewing cabinet. I bought a plastic rolling storage bin with a thick, hard top at an office supply store, I keep a small cutting mat/pressing surface on it near my machine. I'm always looking for better ways to organize!
Oh...as for all those little snippets of fabric and thread...I pin a piece of scrap cotton batting to my shoulder and put it there. Just don't walk out of the house with it!:D