Wait until you get to the Tower, that's just after you complete the first mission.
When you are up there, you'll be with several other players online, simply hit
(the right stick) in a player's direction and then go to "Inspect Player".Thanks to QuickMythril:
You can also go to the menu (
), then roster (
), and if someone on your friend list is playing Destiny at the moment, you can then press
to inspect them.