Joining the Vigil of Renarion is a simple process.
Finding an Officer.
Simply all you need to do is find anyone of the guild and ask them. They'll redirect you either to the forums (if no officers are online) or to one of the officers. If you are directed to an officer, they will ask you a few questions before discussing with you how to proceed for your in-character interview!
The Current Officers are:
Lord Arthur Ravenclaw (Marshal)
Vacant (Ranger-Captain)
Vacant (Alpha-Prowler)
Vacant (Chief of Medicine)
Post-Interview Details
Okay, so there are a few things you need to know about what happens after a successful in-character interview. First of all, you will become a Aspirant in rank. This is a rather precarious rank, and it has some rules attached to it. So see the Code of Conduct thread for the restrictions on the Aspirant rank.
Secondly, you will need to level up to at least 70 in order to be eligible for promotion from Aspirant to one of the proceeding guild ranks!
Beyond that, you will be expected to familiarise yourself with the rest of the guild, its rules, lore and so on forth. But not to worry, all of these things are easy to learn, and much of it is found on these here forums.
Good luck!