Gas furnace maintenance should be performed by the owner, without calling a professional and spend a lot of money. You can clean and check the heating system for problems all by yourself, and only if there is a problem you could call someone with greater expertise.
You should check the gas furnace once a year, just before the cold season.
Shut the furnace power off before checking it. Turning the gas valve off will also shut the pilot light. You will need to relight it after you have finished the work. More modern systems will relight it automatically.
After you have turned off the gas, remove the panels. Remove the screws or clasps. Locate the filter. It may be located in the duct work or inside the furnace. Check the filter and replace it if necessary. Be careful to replace it with an identical one. Mind the airflow direction.
Clean off any dust and debris from the furnace using a vacuum cleaner. Be careful not to damage any parts in the cleaning process.