I think the best advice I can give a new healer is, if you get agro, run to the tank. If you start taking damage, don't run away, run to the tank. focus on your healing first and foremost. Adding DPS is nice, but if you can't keep people up, than you aren't healing. Though those are all common sense things, the most important, bar none is to never take your role as an easy one. Even if you are familiar with the content, something can always throw a wrench into things. Be ready, be adaptable and always ask advice!
There are tons of advanced healing methods to get into, but that first reply also has the best advice, get out there and do it. Make mistakes, overheal, ignore mechanics...but learn from those, so that you don't do them again! Have fun!