You have your home air ducts cleaned if there is visible mold growth on sheet metal ducts or other components of your heating and cooling system. A point to consider for mold detection in heating and cooling systems is that many sections of your heating and cooling system are not accessible for visible inspection. Ask the service provider to show you any mold they say exists.
While some substances look like mold, a final determination that it really is mold can only be made by an expert and may require laboratory analysis for determination. A microbiology lab test, costing about $50, will tell you if the sample you send them (on a clear strip of household tape) is mold or a substance that resembles it.
For insulated air ducts, if the insulation gets wet or moldy it should be removed and replaced because it cannot be cleaned effectively.
Mold growth will reoccur if the conditions causing the mold growth are not corrected.