An annual safety inspection of your gas furnace by a licensed heating contractor is always recommended, but there are some things you can do yourself to ensure your home and furnace is ready for winter.
Test your carbon monoxide detector. Replace the battery. Every home should have one.
Check the furnace area for any combustibles stored nearby. Move these out of the furnace room. Remove anything that could restrict airflow to the furnace. Check all supply and return air vents for blockage. Clothing, lint and furniture are common obstructions.
Check for black soot on and around the furnace. Black soot is a sign of improper combustion caused by a defect in the furnace or vent system. If you find black soot, don't operate your furnace until it has been inspected and repaired by a licensed heating contractor.
Disposable fiberglass filters should be replaced and electrostatic filters should be washed at least every three months. Clogged air filters can significantly restrict airflow and hurt the performance of your heating system.
You can also check your ductwork for leaks when the furnace is running. Slowly run your hand around the outside of an entire duct run to feel for escaping air. Check the return duct by running a piece of tissue along the sides. If you feel the tissue being sucked in, you have a leak. Use ductwork-approved foil tape to seal those leaks.