The Arena works pretty simply. The rules vary, well can, but mostly everyone sticks to the same ruleset, give or take some changes. It is turn based, and works on a mostly logic system. Can you do whatever you are attempting based off your previous actions plus your characters ruleset? That's gonna be the basic process no matter what.
Mainly, anything you wanna know, just ask simply. I suggest reading some of the current and previous fights to get a good grip. There are some magically inclined fights and some melee based fights as well.