The technician will usually confirm the basics you've checked, then move to the burner or ignition, the controls, the safety switches, and the pump or blower. On an oil system that means the filter, nozzle, and electrodes; on gas equipment, the igniter, flame sensor, and venting. Clear a path to the basement and the tank before they arrive.
Most repairs that bring the heat back need no permit. If the visit ends with a new burner, a replaced tank, or new gas equipment, permits come into play: the Building Department issues gas permits through Abington's OpenGov portal, and the Fire Department handles oil burner and tank permits. The contractor should explain which apply and file them.
If the system is old and failing, you may hear a replacement suggestion. Asking for a temporary fix that gets you through the night, plus a written proposal you can compare in daylight, is entirely reasonable.