You cannot unless they "ping" them for you. I think it's shift-click on the hp bar or skill icon, for instance, which might announce in party chat:
"My health is 550 of 550."
"I am using Resurrection Signet on Kevin32!"
"Kevins Opponent is using Meteor Shower!"
"I am wielding an Overpowered Scepter of Pwnage."
There is also the option of pinging their entire skill bar, but really that's too much information for random arena. You should not ask your teammates to ping their build.
You could watch their action bars, but if you're spending all your time doing that, you're probably not helping the team.