Is it in your Items or Etc. tab? Eden Group Mark should be in your Items tab if you registered for Eden Group. The Eden Group Merit Badges in your Etc. tab are different.
If it's the Eden Group Mark, you use it like any other item: double-click or hotkey. It has a 30-minute cooldown (in-game time, not real world time). You can't use it while sitting, but if you try to use it while sitting, it will count as a use, so the cooldown will start. You know if it's currently in cooldown when you try to use it, and you get a notification in your chat bar that you can't use it for X seconds.
Edited by MorseCoder, 28 February 2015 - 06:13 PM.