How can I turn off the green light indicator on my AirPort Express?

Duct Tape

The Zed,

You have two options and you probably won't like any of them.

Using the Airport Utility, click on the AE then "Base Station", then "Options". That will bring up two options for you AE green light, either keep it green at all times or only light up when it is being used.

The second option is put some tape over it.

Hope this helps.

Just unplug it

I doubt the you can disable the status light while your AirPort Express is being used.

You can't. But a piece of aluminium tape will stop any and all light.