Locate the freon lines that go into the supply plenum. This is located just above the air handling unit. You will see that one of the panels for the supply plenum will have screws along the sides and top. Remove the screws with a cordless drill, and put them in your pocket so you do not lose them. Remove the panel to expose the evaporator coil.
Go to the thermostat and turn the air handling unit off so that air will not blow during the evaporator coil cleaning. Turn on your flashlight and look at the components of the coil. Do not physically touch the coil. Look at the drain pan to make sure it is not full of water, and that the drain is free of obstructions. Look at the coil fins for bent or damaged fins.
Take your shop vacuum and stick the hose into the plenum opening. Turn on the vacuum, making sure it does not touch the evaporator coil. Take the feather duster and wipe along the inside of the plenum to take off any dust that has collected over the year. Any dust that falls will be sucked into the vacuum. The rest will be trapped in the feather duster. Keep the vacuum running.
Take the air nozzle of your air compressor and blow along the evaporator coils in short, back-and-forth motions. Using compressed air is the only way an evaporator coil should be cleaned, because it avoids any chance of damage to the coil. Keep the vacuum running for five minutes after you have finished blowing air across the coils.
Check the drain pan for any debris left over from the cleaning process. Use the shop vacuum to remove any debris from the pan. It is important to check the pan for debris, because a clogged drain could cause the pan to overflow, ruining the air handling unit.
Turn the air handling unit on to watch the air blow across the coil. Reinstall the panel and tighten the screws with your cordless drill. Resume normal operation of the central air-conditioning system.