You must have Elizabeth as one of your names (middle, first, even last name if it applies). Spelling variations of Elizabeth (Elisabeth, Elizabyth, Elisabethe, whatever) are fine. And as pleased as I am to note that Elizabeth has given rise to dozens of derivative names, I'm afraid that Lisas, Beths, Elises, Elspeths, Betsys, Bettys, Besses, and other such "stand alone" variations will have to be excluded. Sorry about that.
Secondly, you have to put the ring code on your website and make sure it works. WebRing (where this ring is hosted) has facilities to help you make sure everything is in order, and it's your responsibility to fix the code if it doesn't work. The system is automated and checks for the code, and if it can't find it or it's incorrect, it boots you out of the ring (nearly immediately) or deletes you from the "waiting to join" queue after a certain length of time.
Your site can be almost anything, but it should be personal (a business site would be okay if it's solely owned and there's an "about me" or similar on the site). Your site should be no more racy than an "R" rating, and "PG-13" is preferable. No "under construction" sites or sites without meaningful content, please!
Your site may not have anything X-rated (artistic
nudity is fine, but only if there are sufficient
notices for parental guidance; if you have any
questions, feel free to ask), can't actively promote
hate, violence, or cruelty to animals, or clearly
promote or link to material such as illegal software
That being said, I've been running webrings since
1997, and I've seen literally tens of thousands of
websites of all kinds, and I've only rarely seen
any that I would refuse on the basis of content (I
normally only reject sites if they fail to meet the
criteria for the ring, i.e., if your name isn't Elizabeth
you wouldn't qualify, or if they don't have a working
ring code in place). Rejected sites may reapply when/if
they meet the guidelines. I don't hold grudges.