When your furnace stops working in the middle of the night on the coldest night of the year, you want nothing more than to make sure that you can get it running again so that you can be nice and warm. There are several things that you can check to see if you can get it back running as soon as possible.
One thing you should do is check to see if there is a problem with the circuit breaker. You want to make sure that the breaker is still on and that there is still power to your furnace. If the circuit breaker has flipped off, turn it back on and see if your furnace turns on. If it doesn't turn on, then go and turn your thermostat up. If the furnace comes on and the circuit breaker immediately flips off again, don't turn it back on because there is a problem that needs to get fixed and the circuit breaker has shut down for a very good reason. Wait until you can get a professional come in and look at it for you.
Emergency Shutoff Switch
Your furnace has an emergency shutoff switch on it. It may not be directly on your furnace, it may be near the furnace, usually up high so that nothing can accidentally turn it off. Check it out to see if it has been turned off or if it is still in the on position. Generally, the shutoff switch is something you can use to turn the furnace off if something happens to it, but it does occasionally shut itself off. If it's off, turn it back on and see what happens with it.
If you use propane, kerosene, or heating oil for your furnace, you should check to see if you still have fuel in your tank. There should be an easy-to-read gauge on your tank, either on top of it if it's an external tank or somewhere nearby if the tank is in your house. Check it out to see if you still have enough fuel in your tank.
If your furnace has stopped running in the middle of the night, you want to make sure that you can stay nice and warm. There are things that you can do to get it running again, but if nothing you do works, you need to call an HVAC (heating, ventilation, and air conditioning) service so that they can take a look at it for you and, if necessary, get started on a heater installation.