The Vestige can arrive at the Arena through exploration or by following the quest "Over the Edge." Either way, when they approach the Arena, they are greeted by a Khajiit named Balag at the other side of a bridge leading into a small city created by trainers and fighters. Balag explains there are three divisions: Swordmaster, Sorcerer and Summoner. Zara, who is the Division leader for the Swordmasters, is standing closest to Balag in a circle surrounded by braziers.
Because Feluni, who runs the Arena, capped the number of combatants, the Vestige must beat one of the current combatants in a match and take their credentials. There are three choices; some dual-wield axes, but all Swordmasters are melee fighters. Talk to one of them and ask to fight. Beat them, then head back to Zara. The Vestige can head down the path across from Zara to Tholbor, the leader of the Summoning Division. He also asks the Vestige to defeat one of the current combatants.
The summoners use bows and summon lions to fight for them (even though some of them will say they just learned how to conjure wolves). Malarel is the final leader. She leads the Sorcerer Division. Again, the Vestige must spar with a combatant. The sorcerers use the Sorcerer class buffs but are easy to defeat. Heading northwest from Malarel and up the stone steps, the Vestige brings their credentials up to Feluni, who is between a tent and the door to the Arena. She asks the Vestige if they have a stage name, to which they reply with their name. She decides to call the Vestige "Mysterious Stranger" because it has more intrigue and dramatic flair. She gives the Vestige 270 and tells them to get moving if they want to become Grand Champion.