How can I debug a Firefox extension with Firebug?

Please see MDN - Building An Extension - Debugging Extensions, which shows what tools Firefox provides you with to natively debug extension, also take a look at Dive Into Greasemonkey - Debugging User Scripts (PDF, p.13) which is aimed more specifically at your request.

Other than that, see How to debug a Greasemonkey script with the Firebug extension?

Use Chromebug it's firebug for extension development, witch will give you the full ability to inspect debug firefox it self and all firefox extension as if it's a webpage :)

1- install the latest version from here: http://getfirebug.com/releases/chromebug/

2- Winkey+R to open run then type firefox.exe -chromebug this will run firefox with chromebug

3- for more information visit http://getfirebug.com/wiki/index.php/Chromebug