How do you make an arena?
I use a rather simple set-up. I dig out a room; sometimes with a lever-controlled channel-and-retracting-bridge down the center, if I'm planning to train Markdwarves there. Then I set up some of my prisoner cages, using 'b' - 'j' - select a spot - 'x' - select a caged prisoner - 'Enter'. I usually set up fifteen caged Goblin prisoners at a time, or correspondingly
fewer tough opponents, such as five caged Troll prisoners at a time.
I build a bank of levers outside the room. The cages are hooked up to the levers, with as many opponents as I want to fight simultaneously (eg: three Goblins, or one Troll) all hooked to the same lever... so I might end up (for example) with five levers in the corridor, each lever hooked up to one Troll cage or to three Goblin cages.
I set up a set of air-locks in the passage leading to the arena, with the doors set to keep Pets out... no sense getting my Wardogs killed in training fights. I also set the doors of the arena itself to keep Pets out.
I disarm the Prisoners via the Stocks menu ( 'z' - weapons - 'Tab' - change 'F's to 'D's... but be sure not to mess with your own Dwarves favored weapons, which will appear in the same list) but I let them keep all their Armor, since it makes the fight last longer and therefore yields my Military Dwarves more experience.
Then station a squad in the room, lock the door, open the retracting bridge (if Marksdwarves are involved), and start releasing the prisoners... one strong opponent or one group of weak opponents at a time.