You should really, *really* read the FAQ (the link is the first post on this board) before you ask how to join. (psst, some people get irritated by that particular question).but to help you out...you need to have Ultima Online, a PC game that you pay a monthly fee for as well. then you have to wait around in The Arrow tavern (in Tel'Ruid, on Ultima Online) and RP with the TGC members. After a while of interacting with the guild, one of them will ask you if you would like a sponsor (they must get to know you first). Then it could take a very long time to get in the guild as a member. It just depends on the person.
Oh and, you should post your character history here (where you came from, etc) like a mini-bio. Saying you're from elven background isn't really telling the elves much about your character.
Good luck with everything. I wish you the best. =)