The arena can be accessed via the fights menu (arena icon) or the arena building in the city.
In the arena three random players from the hall of fame are ready to fight that have a similar rank to your own character.
If you defeat your opponent, you win honor points for the hall of fame and XP up to ten times a day. The gain in honor depends on the honor difference between the opponents. If this difference is too big (from about 950 honor), you don't win anything. If you move your mouse pointer over the profile picture of the opponents or tap a little longer, you can see where theirs strengths and weaknesses lie.
The fights are turn-based. With each round, "rage" increases, which ensures that the blows become more powerful with each round and deal more damage.
If you want to specifically attack certain teammates, this is possible via the hall of fame. However, these fights are not rewarded with XP.
After each fight you have to wait ten minutes until a new arena fight is possible. You can skip the waiting time by spending a mushroom.
Past fights can be watched again by clicking on the "Fights" tab in your mail. Fight reports are saved for a certain time there.