To clean furnace coils use a combination of compressed air and soft brushes to remove loose dirt and dust. Specials coil cleaning solvents can also be used for this purpose. Also, use biocides to kill any mold growth inside the coils, recommends SFGate.
Furnace coils tend to accumulate dust, dirt and debris over time. The best way to remove these is by vacuuming away the dust using the hose attachment of the vacuum cleaner. In addition, a soft coil cleaning brush with a long handle can be inserted between the coils to remove hidden dust. Vacuuming and brushing are to be done gently as possible; otherwise, the coils might get bent, hindering optimum furnace performance, according to eHow.
Alternatively, use special coil cleaning liquids to remove dirt and other debris from the coils. Keep a pan underneath the coil to catch the cleaner so that it does not get into the heat exchanger or ductwork. Also, be careful when using these solvents as quite often they contain acids.
To remove mold growth from inside the coils, use biocides. These also prevent mold growth from recurring. Finally, remember to disconnect the furnace cord from the power source as a safety precaution before beginning the cleaning process.