Why would home heater not work?

If it is gas, the most common problem is the thermocouple. This is what keep the gas valve open. It is a small silver looking wire, 1/8 of an inch diameter that runs from the gas valve to the pilot light. The pilot flame should touch the end of the thermocouple. Of course it can be a lot of things. Power, there can be a fuse at the furnace that may have blown. There will be a box with a light switch and a screw in fuse. The switch may have been thrown.