One of the most common reasons why a furnace stops working is very simple -- you may be out of propane. If you have not had the tank filled lately, or checked the gauge, there is a high probability that this is the problem. You will need to have propane put in the tank and then the furnace will need to have the pilot light relit. Make sure you light the pilot immediately.
Another reason a propane furnace won't turn on when you click the thermostat can be the pilot light. From time to time, pilot lights can go out, especially if you have a draft near the furnace. If you have never lit a pilot light before, call your gas company to do this for you. If you have, follow the instructions on the furnace and light the pilot light. Wait a few minutes and then click the thermostat -- the furnace should now work.
Thermostat problems may also be the culprit if a furnace won't heat. Check the propane levels and the pilot light. If these are fine and the furnace still does not click on when you turn up the thermostat, it is likely that the error lies in the thermostat. Call your furnace company or a local heating and cooling repair company to have this replaced. They will be able to test it to confirm that this is the problem.
Problems with the thermocouple and other interior parts can also prevent the furnace from working properly. Another serious issue occurs when the pilot light simply will not stay lit. This can be dangerous and may place your home at risk for carbon monoxide. If you have gone through the previous troubleshooting steps and the furnace still does not work, it's time to call in a professional. They will be able to correctly diagnose more serious issues.