The battles fought in Arena are exactly like normal, except all troops (including heroes) are set to level 15 and have no traits, shared type or kingdom bonuses, kingdom stat bonuses, or hero classes.
Regarding forming teams for the Arena:
The draft order is the Common choice, the Rare choice, the Ultra-Rare choice, and then the Hero weapon choice.
All troops are level 15. This means you can use troops that haven't been leveled or aren't even in your collection.
For the Common, simply try to pick a troop that isn't next to useless (many Commons are).
For the other picks, firstly try to get as many colors as possible. If you have a Brown Common, don't get a Rare that is also part Brown if you can help it.
The ideal goal is to have all six colors between your troops, but five will do in a pinch.
Choose a weapon that suits the team - this is particularly important for filling out colors, but if you can pick one that has some synergy, even better.
(Since weapons are unlocked largely through Mana Mastery, try to spread your points evenly when you level up, so that you have a decent range of weapons to use in the Arena.)
Change your team order how you want. Just remember you can.
Mana generator troops are good pickups since you can choose a hero weapon that benefits from them and achieve automatic synergy (assuming you don't have or get another troop that is equally suitable). This is particularly useful since the hero weapon will likely be one of the stronger abilities in the team.
Avoid troops that need synergy or special conditions to function well. Something with a condition such as 'triple damage if the enemy has Hunter's Mark' or 'boost damage based on gold collected', for instance, is going to be quite difficult to fulfill without a specific team. Similarly, troops that work best against threats that are typically Epic rarity or higher (such as Daemons or Dragons) aren't going to be as useful.