Materials required: None
Time required: about 2 minutes per year
Savings: $30-$60 per year (depending on your furnace, your location, and gas prices)
GHG reduction: about 0.15 to 0.30 tons per year
I live in a moderate climate (Vancouver, BC, Canada) and only require artificial heat about 7 months of the year (from mid October to mid May). For the other 5 months of the year I turn my furnace off completely, including the pilot flame. There are occasionally some cold days during that period but we usually just wear extra clothing and leave the furnace off. Throughout much of the US the heating season is shorter and potential savings are even higher.
To turn off your furnace completely, look for a valve in the gas line to the furnace. Simply turn the valve handle so it is angled 90 degrees to the pipe. If you like, you can check your furnace to ensure the pilot flame goes out.
To turn your furnace back on, turn the valve handle parallel to the pipe and re-light your pilot flame following the furnace manufacturer's instructions (if you don't have the manual for your furnace you can probably look it up online, or just wing it... they're mostly the same). As a reader has noted, there is no danger if someone turns the gas valve back on but forgets relight the pilot flame. There is a thermocouple that prevents gas flow unless a flame is present. You typically have to hold a button down to get the gas to flow when re-lighting the pilot flame, and keep holding it down until the thermocouple warms up.
That's all there is to it. For more ways you can reduce your impact and save money doing it, see my website, www.IWillTry.org.