Because flies are sensitive to air currents, a rolled-up newspaper is actually a poor substitute for a mesh fly swatter. Instead, put some surgical spirit into a plant mister and spray the fly. The stuff kills on contact - but be aware that it may mark some finished surfaces.
Or spray the fly with hairspray to immobilise its wings and then you can swat it. But don't do this near any good pieces of furniture.
hairspray vs flies