Depending on your HVAC system, you may have a portion of your ductwork as large rectangular pieces. Other parts of your ductwork system may be smaller, flexible circular ducts. To improve air quality in your home, you should periodically clean out the inside of your larger rectangular ducts. Small flexible ductwork often times can’t be cleaned with destroying the duct itself. You should consult with a residential HVAC professional to provide guidance on whether you have a system where cleaning the ducts is appropriate.
A good way to see if your ducts are dirty is to open each vent in the home, insert your hand with a digital camera as far as you can, and take a photo. This will give you a quick visual of what the inside of your ductwork looks like.
Hire a professional company to assess your ductwork to see if a cleaning is appropriate. Here is a video from the NADCA.