Check your damper handle to see which position it is in. If the handle is in the closed position, your flue damper should be closed. If the lever is in the open position, your flue damper should be open. The lever position does not guarantee the damper position however, and many people forget which direction is which, so a visual check is a good idea. Most damper controls are of the pull chain variety. In this case, the chain is in the lower position when the flue is closed and in the upper position when the flue is open.
Visually inspect the flue damper during the daytime to see if it is in the open or closed position. Move the control lever to the open position. Look inside the chimney toward the roof to see if any daylight is visible. If you do not see daylight, move the control lever in the other direction, and check again.
Climb the roof and check whether your flue damper is opened or closed. Have an assistant work the control lever below, and relay the damper position to him. If there is a problem with the flue damper, you should be able to locate the cause from here.
Watch for heat backing up into the house from your fireplace opening when a fire is burning. While woodburning fireplaces release smoke into the home, gas fireplaces produce only heat. If you have a backup of heat, it indicates that the fireplace damper is in the closed position and that heat and fumes cannot escape through the chimney. By the same token, if you notice a large amount of cold air or you are able to feel a breeze blowing into the room from your fireplace, the flue is probably open.