When you enter an arena the server first sees that you've entered a PVP floor and makes you hostile to everyone and everyone hostile to you. That includes your teammate. There's a lag time between that and when it's seen that you are on the same team and makes you friendly.
If you do arenas, you may have noticed this before. If you have enemy nameplates on, when your partner enters after you for a brief moment you'll see the name plate pop up in red. That's the lag.
First you'll need a macro.
/tar (the name of the teammate you wish to harm)
/cast arcane power
/cast presence of mind
/cast pyroblast
The abilities will differ from class to class. Just make sure it's an instant cast. Bind it to a spammable key.
When the queue pops, you need to get in the arena before your partner does. Once you're there, stand in the back of the room and mash the key. Once your partner enters she'll get blasted. "That's for going AFK in queue last match!"
Edit: for those who are confused, this works with any class with an instant cast, the above macro is just the one I use on my mage, the main part you need is the "/tar (player name).
Also, this can be used for advantages as well, as Soul Eater's pointed out in this thread. It's been noted that if you're a warlock, you can use Curse of Recklessness your teammate, which is basically a Fear Ward (in fact, when Curse of Recklessness is up they're immune to Death Coil too).