Well the best healer is a priest, a holy priest. You should build up your talents on shadow untill you get to lvl 70, then go to a priest trainer and unlearn your talents. Set them like this:
It may look wierd that i put 5 talent points on "Wand specialization", but when you are healing you use your mana. And when you are out of mana you can shoot the target with your wand while you regain mana (you don't use mana when using wand).
For healing you should have a weapon and armor that increases your spell damage and healing done, intelect, spirit and critical strike rating.
Use better healing spells like greater heal, but when you have very low mana and you need to heal your target, just spam some low healing spells.