To clean an air duct you can use a shop vac to suck out most of the dirt, debris, dust, lint etc.
However to fully clean the air duct you need a long hose attached to the shop vac.
You can also hire an air duct cleaning service and a lot of HVAC companies who do repairs on air conditioners, furnaces etc have the ability to clean air ducts.
The professionals can get your air ducts much cleaner than you can at home.
Remove vent covers and wash them. Remove your vent covers with your screwdriver.
Cover vent openings with paper towels. Cover the openings to your supply registers with a few paper towels.
Loosen the dust.
Vacuum it up.
Change your air filter.
Replace vent covers.
Remove the vent covers by unscrewing the corners, then place them in a sink of hot, soapy water or water mixed with basic household cleaner.
Let them soak for only a few minutes, clean them with a microfiber cloth, then rinse them off with cool water.
Turn off the power connected to the heating and air conditioning system.
Unscrew the air duct covers or grilles from the walls.
Use your brush to clean the grates thoroughly.
Vacuum the ducts as much as possible. Consider renting a heavy duty vacuum for this purpose.
Clean the grilles in your ceiling.
Experts advise having your air ducts cleaned every 2 to 3 years to prevent many maintenance and health problems before they start.
However, homes with pets or children with allergies should have their air ducts professionally cleaned more frequently than the recommended average.