According to what we saw on the PTR, it should come default whenever you head into an instance, but if you want to see aggro all the time, you can go to the Interface options, and flip "Display Aggro Warning" to always. Checking "Show Aggro Percentages" will give you a little percentage at the top of the target frame, showing just how much aggro you're getting from whatever you've got targeted.
If you've used a threatmeter before, you know that if you do pull aggro, you'll want to a) stop healing or doing damage immediately, and b) pop any aggro-reducing trinkets, abilities or talents you happen to have, like Feint or Disengage. Of course, if you have used an addon like Omen in the past, odds are you shouldn't get rid of it -- the ingame Aggro Warning is pretty thin, so odds are that your guild will still require Omen anyway for high level raiding. But as a simple heads up when you've got monsters about to come your way, the Aggro Warning does its job.