Stick the plastic to the ceiling using blue painter's tape. The tape won't damage the ceiling surface when removed. Use a thick painter's tape for added strength. Apply pieces throughout the area where the plastic meets the ceiling.
Hang plastic from an unfinished ceiling area by nailing it to the rafters. Find a beam that extends across the area you want covered by the plastic. Hammer a nail into place approximately every foot. Remove the nails when you want to take the plastic down.
Attach the plastic along the ceiling by pressing thumbtacks through it and into the ceiling at the rate of one every foot or so. For lightweight plastic, you may be able to use fewer tacks. When you finish, remove the thumbtacks and fill in the holes with tiny dots of putty that match the ceiling color.