How do I fix this problem? My furnace comes on but does not blow air.

I am going to be honest you should get a furnace company to come in and look at this problem right away. It can be as simple as your thermostat and it may be the relay or the electric motor either way it is not good and can cause serious long term damage to furnace and in some cases actually be dangerous. In the case of a natural gas furnace the heat exchanger may become over heated and crack which can cause irregular amounts of carbon dioxide into the air putting you and your family at risk. An electric furnace can become over heated and if the safety shut off does not work properly cause fire. Please take my advice and have some one who actually knows furnaces have a look.
James

If you turn the fan switch to on at the thermostat will the blower run? If yes, you can let the blower run all the time and the heat will cycle on and off as it needs to. It will give you heat until the problem is solved.