Furnace care splits into two kinds of work. Some tasks belong to the owner, and some belong to a trade visit. Sorting the list before the heating season keeps you from calling for a job you could have done yourself, and from attempting a job that needs tools, training, or a permit.
Owner tasks
Keep the area around the furnace clear of stored items, boxes, and cleaning supplies. Check the air filter against the manual and replace it on the schedule the manual gives. Confirm that the thermostat settings produce heat when you ask for it. Look at the outdoor vent termination for debris, and clear loose leaves or snow from around it without reaching into the opening. Note anything you can see or hear, and write it down with the date.
Trade visit tasks
Combustion testing, gas line work, burner adjustment, heat exchanger inspection, and any electrical work inside the cabinet belong with a trained technician. So do repairs that require disconnecting the unit, opening the gas valve housing, or changing controls. These jobs carry safety risk and often need a permit under local rules.
What to ask the technician to write down
Ask for a written list of what was checked, what was measured, and what was left alone. Ask which items you should watch between visits. A short written scope gives you a reference the next time you call.
If you smell gas
Leave the building, do not operate switches or light flames, and call the gas utility or the emergency number from outside. This is a safety step, not a repair step, and no owner task replaces it.
Use the walk-through
The fall furnace walk-through on this site lists the owner-side checks in order. The gas furnace service life page explains how age feeds into planning. Read both before the first cold day.