The Galactic Coalition (GC): The main lightside group and only lightside group which currently engages in fleet battles, the Galactic Coalition was designed to counter the threat of the Empire and to help out the citizens of the galaxy. Pretty much we are the "good guys" kind of like the New Republic from the Expanded Universe. We accept both Jedi and non-Jedi, but currently can not train Jedi, however you can belong to both The Jedi Order and GC at the same time. 3rd largest fleet group at this time, though kind of tied with the Black Dragon Empire for second place.
The New Order (TNO): The Empire of this time. Designed to uphold the principles of Palpatine's New Order, TNO is the major government right now, pretty much controlling the galaxy. They are much like the Empire from the movies. Inside TNO is The Naboo Sith Order (TNSO) although they are no longer based on Naboo. If you want to be a sith, join here. They are the undisputed leader of all fleeting groups.
The Black Dragon Empire (BDE): An empire, with a large quantity of planets, all bunched up together in their region of the Outer Rim. They have numerous religious principles and I have to admit I don't really understand them all. But if you wanted to join them, they would be more than happy to explain. They are the second largest fleet group on TRF at this time, though GC is rapidly catching up to them.
Vinda Corporation (VC): A corporation which is neutral in the galactic wars, although it does maintain a fleet. It is based out of the Corporate Sector and is really cool. If you want to work more on character developement and not have to worry about galactic politics or fleeting, these guys are probably the people you want to join.
The Jedi Order (TJO): The Jedi Order is led by Leia Organa Solo and is the only group of active Jedi at this time. Previously disrupted by a Sith attack on their base on Naboo, the Jedi Order has recently seen a rise in membership and has become much more active. It is expected that they will soon begin to play a role in galactic politics and by the time of the next galactic war (which could happen at any time, but hopefully not for a few months) most people expect them to have enough power to play a significant role in the war.
Thats the major active groups right now, though I think BDE has suffered a momentarily lapse in activeness. There are also several smaller groups which would no doubt welcome new members, such as the Caprician Regency and the Cree'ar Dominion. For information on the Caprician Regency ask Omnae (AKA Simon Kaine). For information on the Cree'ar Dominion ask Ahnk. Some other people may be able to provide more information on the Capricians of Cree'ars, just not me.
cool. It was the abbreviations that got to me. I'm wanting to be in the Jedi order, but apparently, I can't be trained until a month from now, but I can wait.