Best way to train for Team Arena is just play on an alt. I'm starting to just warm up on mine. Sure you don't get REQs and XP on your main for a couple games but oh well.
I would not recommend that either. The only people that should be playing on ALTs are people who are hitting low tier champions and finding a match begins to prove difficult. If you want to get better, you should be grinding on your main.
You want to be playing people at your skill level.
If you play team arena and want to get better, here are some things you can do...
Positioning:
~Always be mindful where you place yourself. Will it help your team? Can you get away if things turn to shit? You need to constantly put yourself in a spot that will be effective for your team. You also need to take into consideration that if shit hits the fan, that spot should make it harder for the other team to kill you. It should allow you to survive for as long as possible while also being able to remain combat effective for your team.
Gun Game:
~Let's be real here, gun skill helps. You just have to find a way to get better for those individual fights that will occur in arena. If you can't win your 1v1s, then do not expect to get far in arena because there will be battles that you will have to win on your own to make those "plays".
Theater:
~Yo this exist now and it is not only there for you to go back and watch your montage moments. It is there for you to study as well. Learn positioning yo! Learn why you lost that battle you did. Ask yourself what can you do better.
Purpose
~When you play arena, you need to have purpose on the battlefield. From spawn you should have an idea of what you are going to accomplish. Don't venture to any part of the map without purpose cause you will just be confused and look stupid. Take into consideration what spawns on the map. EVERYTHING is viable. Boltshot? Fantastic gun. Hydra? Has a higher skill ceiling, but if used right, you suppress people. EVERYTHING has a purpose and works.
Engaging
~Shoot anything that is not on your team. If you see an enemy, put some shots on that mofo. When you bleed there shields, they tend to be less inclined to fight. Get those damage numbers up! You need to keep in mind, if you break there shields, DO NOT CHASE unless you have a teammate near you and you KNOW for sure you can secure that kill without having to trade. Sometimes trading is inevitable, but keep that in mind. A lot of people tend to see someone with no shields and decide to chase, it is never wise to do such a thing.
When you break their shields, you already know they are going to call for that backup so if you cannot chase, then keep a mental note where that person was and that they will be out of the fight for a few seconds. If help comes, then you better be ready to back away cause they might challenge with that help.
Communication
~We all know this is a plus, but I laugh when people say just to call out. Calling out is not enough. You need to let your teammates know where you decide to go as well. If you are going X area, then say you are going X area. If you see an enemy X area, try to say where he is going from X area. As in. That guy is in X area going to X area. If you are going to push, then ask someone to come with you. Communication is only as effective as you make it be.
Times:
~Everything is on a clock. Keep in mind as to when it spawns.
Powerups:
~Overshield and Camo are HUGE. Getting those on the map are essential. Controlling those can influence you in controlling power weapons. Get those powerups and NEVER ignore them. If the enemy gets them, MAKE it your job for them to die. Killing them is pivotal.
This is only brief cause I wanted to be as short as possible. I will not be surprised if I did not cover everything.