Do a bunch of battlegrounds. That's how i learned to heal. The health bars were flopping all over the place, so crazy and hectic (wintergrasp) that it made predictable PVE so much easier (still have people that thing fire will make their arrows flaming arrows, and therefore do more damage... it doesn't). What it also does, it gets you used to people dying. And once you get over the fear of people dying and knowing that sometimes, you just can't save everyone, you'll lose that fear a bit.
Mind you, I haven't healed a heroic as a 829 ilevel healer, I tiptoe into harder things - but mainly, this expansion, is that I'm learning to manage my mana. I can easily go OOM as resto druid, and so I'm more concerned with being able to toss a heal. And so after doing a normal DT with all 110s (random) and having to drink like 8 times... I still have work to do.