Generally they leave things laying around during construction or throw it in the general dirrection of a large pile; and if you are lucky they will haul most of it off at the end. when we were building, we lived on the site, and kept things tidied every day. We bought large contractor garbage bags and put trash cans inside the house. We were mainly the ones who used them, though, in the evening when we went to tidy up. Contractors are not tidy men. They are busy measuring and sawing and hammering, and don't even notice the debris, unless it's in their way. I think they very much appreciated that we tried to help keep the site tidied.
We bought a rolling magnet to run around the site with to pick up nails and metal debris. Sometimes they will contruct a wire fence to put things that blow, such as styrofoam, but they don't really care if it blows away.
My sister is doing a major renovation now. She rented a large rolloff. Her workers are carrying the debris out pretty well, but only because it is in their way in the house.
Their idea of cleaning up after themselves on a site is probably not the same as yours.