What should I use to protect and cover my floors during construction?
If you don't have any heavy duty canvas type drop cloths, then use a couple of layers of red rosin paper. Tape the seams and around the perimeter to hold it in place. Keep an eye on it and tape or put an extra piece on any areas that get ripped.  Red Rosin is much better than plastic as it is not slippery to walk on and is fairly tough for foot traffic.