When the heat won't come on, a few simple checks solve a surprising number of cases before you need a technician. Work through them in order before calling for service.
Thermostat and power
Confirm the thermostat is set to Heat and above room temperature, and replace its batteries if it's dead. Check that the furnace switch (it looks like a light switch nearby) is on, and that the furnace breaker hasn't tripped.
Filter and vents
A severely clogged filter can shut a furnace down on a safety limit. Replace it if it's dirty. Make sure supply and return vents aren't blocked by furniture, which can also trip the system.
Gas and pilot
Confirm the gas is on. Modern furnaces use electronic ignition rather than a standing pilot; if the burner won't light, the igniter or flame sensor may need cleaning or replacement — usually a technician's job.
When to call
If the furnace short-cycles, blows cold air, smells like burning, or you smell gas, call a professional. If you smell gas, leave and call your gas utility from outside first.