You can definitely clean with a vacuum or a clean cotton cloth, but cleaning the ducts requires getting inside the ductwork. And getting inside your ductworks is not possible (or recommended) for the average homeowner.
Duct cleaning professionals, such as those at United Home Services, use specialized HEPA vacuums that use the same techniques and equipment utilized in hospitals and laboratories to capture all the dirt, dust, and airborne contaminants.
Using appropriate equipment is very important to ensure that the contaminants present in the ducts don’t enter the air inside your house.