You'll need five tools to clean the evaporator coils on your AC unit: a screwdriver, a stiff brush, a large hand mirror, household bleach and wire. Once you have these tools, make sure you know where the evaporator coils are located. You'll find the evaporator for a central air system located directly above the furnace in the plenum (main duct). Your AC unit may have a plenum that is sealed shut. If so, don't try to open it; it means you don't have an AC unit you can clean yourself.
Assuming you can open your AC unit's plenum, the first thing you want to do is remove the foil-wrapped insulation at the front of the plenum. This insulation is likely taped in place, so remove this tape carefully. You will have to put it all back. Behind the insulation is an access plate. Take your screwdriver and remove the screws holding the plate in place. Once the screws are out, remove the access plate.
Now you should see the evaporator itself. Some can be slid out a bit, even if they have rigid pipes, but be careful as you do so. Use the stiff brush and hand mirror to clean out the underside of the evaporator unit.
You'll also want to clean out the tray that sits below the evaporator. The tray is there to carry away condensation from the evaporator. Take one tablespoon of bleach and pour into the weep hole to prevent fungus growth. If the tray has a lot of moisture, it could be due to a blockage in the drain line that connects the weep hole to the tray. If that's the case, you can open up the drain line by pushing a wire through it.
Once the cleaning has been done, push the evaporator back into place if you've moved it and screw in the access plate. Then you need to re-tape the insulation back over the plenum.