Collecting useful debugging information with ADIC is easy. You only need to know one piece of information for an ADIC-enabled addon and two for any other addon. This is a quick tutorial on how to use ADIC to collect information about your system.
Launch ADIC using the "Collect Debug Info" menu item in the tools menu.

You can click on the "Browse" button to select from your installed ADIC enabled extensions. If an istalled addon does not appear in this list it is not ADIC enabled and you need to ask the addon author for the ID of his addon. This is either a UUID (like {ec8030f7-c20a-464f-9b0e-13a3a9e97384}) or an email address (like adic@youarefunny.addons.mozilla.org). You can also get the ID by finding it in the table at about:support (see image below).

Enter the add-on's ID into the top ID field and click "Check". If the addon is ADIC-enabled the button text should turn green and the second "code" field will disable.

If the add-on is not ADIC enabled the second field will remain enabled. If you put in a bad ID the "Check" button text will turn red.
If the add-on is not ADIC-enabled you can not gather your preferences unless you find the add-on's "code". The best way is to ask the extension's author where it's preferences are located. If not you can try to find them by navigating to about:config and typing "extensions." into the filter. Try to find the prefix of the preferences relevant to the add-on. For example, ADIC has it's preferences at extensions.adic.*. The "code" of the add-on is the value after extensions. For ADIC the code would be "adic". Below I have an example for "HTTPS-Everywhere".

Once you have this value enter it into the second, "code" field and click "Check". If it turns green you are good to go.

Click "Gather Debugging Information" and the bottom text area should populate with the information.
You can click "Copy to Clipboard" to easily grab it all and paste it right into a message to the add-ons author. The "Copy Indented" is also convenient if you are going to paste into locations where you mark code by indenting it. Remember that the information collected by ADIC may contain personal information and it is your responsibility to remove it before posting online.