Close the damper. The damper will prevent some air from leaking out of your chimney.
Fill a garbage bag with fiberglass insulation. Wear work gloves and a long-sleeved shirt when working with fiberglass insulation, as the fibers can come loose and irritate your skin.
Tie the garbage top in a knot or use a twist tie to secure it.
Stuff the filled garbage bag up into your fireplace until it holds and blocks the chimney. If it falls out, fill it some more. Alternatively, you can purchase an inflatable draft stopper at a hardware store and use this to block the flue. It's like a balloon for the inside of your chimney.