people would go in a special forum topic, and copypaste their character. then, the highest level player goes first, saying stuff like:
"I use ability Pounce. it does 3 damage"
where the damage is calculates as follows:
each ability has a Attack Value. Lets say the Attack Value for pounce was 2.
you have offensive and defensive stats, ATC and DEF, which are numbers, usually smallish ones. So does your opponent. Your level, in this case assumed to be 1, multiplied by the Attack Value for your ability, multiplied by the ratio of your ATC, in this case assumed to be 3, and your opponent's DEF, 2 in this example, making the ratio 1.5.
so, 1x2x1.5=3 damage
the first person to run out of HP earns a certain amount of XP for both players, more for the winner. if it is a friendly fight. In an unfriendly fight, double amounts of XP are given and the loser must hand over a small sum of money.
Although early abilities are quite simple, abilities you get at laterlevels and unique abilities have complex logic.
And that's how they fight.