Exactly that. I'm not sure how this works? Do I have persistent character's throughout each tournament/battle or do you have different characters? If someone could give me a short tutorial on how to get started, I'd be eternally in said person's debt.

http://www.roleplayerguild.com/topics/80287-arena-faq-advice/ooc

That being said to answer your question you can have persistent characters if you want, it's up to you whether to canonize a fight or not. It's also up to you if you use one character or many different ones, though having a few characters at different power levels is a good idea so you're more flexible to fight.

Best way to get started is look around the ranked headquarters (these are all in the arena section) or arena chat thread, check out the CS section in the ranked headquarters to get a taste of what sort of information you need for Arena fighting CS's. Once you've created a character with all the necessaries (and worked out what power you want to fight at) challenge someone or let others challenge you and work out a fair fight. Then things pretty much transpire as you expect.

Also read up on T1 Eden Era, as it's the most common fighting method used here and a good starting point.

Any other questions I'll try and answer them, though they may already be answered in the Arena FAQ.

His life is now yours Melon, do with it what you will.