Fireplace dampers are often made of steel or some other metal. They typically have a frame, which fits around the edges of the chimney, a steel plate which fits inside it to seal off the chimney, and some type of handle which hangs down low enough for the user to reach to open and close the damper.
The damper should always be completely open when lighting a fire to allow smoke to escape. Once a fire is opened, it should still remain at least partially opened to keep from smoking out the room, but partially closing the damper may allow more warm air to stay in the room.
Dampers should remain closed when there is no fire in the fireplace to avoid a draft. Also, if you leave the damper open, you run the risk of having leaves, other debris and even a small animal fall down your chimney into your home.