Along with picking one or two healing targets, you should slowly learn to recognize who should be healed. For example, a ret pally makes an excellent "partner," but once they're out of mana their damage drops to horrendously low levels, and you might be better off picking a new target. Casters or hunters with lots of melee on them are often poor choices too.
Melee classes tend to be the best to stick with; they can both takes hits and deal incredible damage. Classes that are mana-dependent and are almost oom, or those that are stuck in a situation where their damage is severely compromised (mage with 3-4 melee on them, hunter trapped in melee), can often be sacrificed in order to keep someone more useful alive.
Takes a while to get to know when you should stay on your current target or switch over to another one.