On a call for heat, the 24 volt thermostat
sends a signal to the control module. The control module will indicate a call for heat with a light on the control either blinking or remain solid depending upon model. The inducer (exhaust) blower will purge all gasses from the furnace and pressurize a pressure switch. Once the pressure switch tells the module to continue, the electronic ignition will energize and send 120 volts to the ignitor. The ignitor will glow and you will be able to see it if viewed thru the small inspection port. Once the ignitor gets hot enough, it sends a signal to the module opening up the gas valve (24 volts). Either a pilot will come on or the burner tube will ignite then spread the flame to all burners. Lastly a safety sensor will be looking for a certain temperature within a few seconds and the furnace will continue to operate and the room air blower will turn on in a minute or two.
What could go wrong? The unit will not run if there is no signal from the thermostat (bad thermostat or broken wire), the control module does not sense a signal from the thermostat (bad control), the inducer does not energize (bad motor), the pressure switch does not close (blocked vent piping, bad switch, plugged condensate hose), the ignitor does not energize (bad control, bad ignitor), the gas valve does not open or there is no gas (bad gas valve, broken wire, no gas), the pilot does not lite (dirty pilot), the burner does not lite (bad burner, plugged orifice, not enough combustion air), the flame does not spread to each burner (bad flame spreader, dirty flame spreader, more bad burners), the flame safety sensor does not detect flame (dirty or bad flame spreader, bad flame sensor, broken wire, bad control), or the room air blower does not energize (bad fan motor, bad control).
Most newer furnaces will have a diagnostic center or control built into the control module. You may be able to view it as it is running thru a small viewing port. Some models will require the removal of an access panel prior to finding it. On the reverse of the access panel, there will be a diagnostic chart that will aide you in understanding any error code recorded (usually a blinking light).