Open all access panels and use a wet/dry vacuum to clean out dust, dirt and debris from around the motor and blower, inside the burner compartment, and from other mechanical parts. Use the vacuum's brush attachment for fan blades and general debris removal; use the crevice tool to get to hard-to-reach areas. Be careful not to jostle or disconnect wires when you're cleaning inside compartments with the vacuum and brushes.
After vacuuming, use a slightly damp cloth and wipe everything down.
Inspect all wires and connections. Use a screwdriver to tighten any loose terminals.
Apply heavy-duty electric motor oil to the fan shaft and motor if there are oiling ports. Be careful not to over-oil your furnace and never use automotive motor oil or 3-in-1 household oil. Check the motor's belt to see if it is loose or cracking. If you see cracks, replace it. Take the belt to your local True Value hardware store to find an exact match. If the belt seems too loose, tighten it down by first loosening the attachment bracket, then pull the belt until it's tight and retighten the bracket. Clean the thermocouple with a cloth. Use a precision duster with compressed air to clean in and around the pilot light.
An old toothbrush or other small-sized brush can help you remove any stubborn dust and debris from fans and other parts. Toothpicks or cotton swabs are good for getting into very small openings on machinery such as the blower.
When cleaning with compressed air, always wear protective goggles and a dust mask.
When gas lines need repair or replacement, call a professional technician for help unless you're absolutely sure you know how to perform this maintenance correctly.