Your old furnace probably works this way.
1. Turn the gas knob to Pilot. Push the knob IN and light the Pilot. Hold for 1 minute and release and the Pilot should stay lit.
2. Once the Pilot is lit, you turn the Gas Knob to ON
3. You then turn the tstat ON and the furnace burner should then light, after a few minutes, once the Heat chamber gets hot, the Circulation fan should then come ON and blow hot air.
4. When the tstat is satisfied, the burner shuts off, Pilot stays lit, and the Fan shuts down after a few minutes of cool down.
That is how the OLD furnaces operated. What Brand and Model furnace? Doug