Whatcha do is click "User CP" at the top of the screen, scroll down the "Group Memberships" on the menu at the side of the new screen (click it, obviously ), put a tick in the "Dragoon Elite Private" box, and click "Join Group". Fill out the form, and click OK.

Then one of the Dragoon Admins will probably add you to the group so you can post in the private area... if they're feeling nice.

Welcome to Zelaron, btw.