How do I tell which faction a pandaren player belongs to?
All players, as of Mists of Pandaria, now have their faction included in the tooltip:
If you're suitably knowledgeable about armour rewards and looks, you will sometimes be able to tell by the style of armour they are wearing as well.
In PVP, the most intuitive way of knowing wether a Pandaren is part of your faction is by checking their nameplate. If theirs is colored Blue, they are part of your faction.
Additionally, in MoP the faction information will be included in the tooltip whenever you mouseover on any player.