Just a couple of other points that I think should be tossed out.
1) Consumables are your friend - Elixir of Healing Power, Elixir of Draenic Wisdom, Golden Fishsticks, and all the appropriate health and mana pots. Healthstone if a warlock is in the group. It's far easier to pot yourself and heal others than to take the time to toss a heal on yourself.
2) Know when to take a potion. You'll learn the fights as you go - in long fights where you know you will run out of mana, take your first mana pot as soon as your mana bar drops low enough that none of the pot will be wasted. Take more every time it cools down. Alos remember that mana pots and health pots share a cooldown - if you're going to have to take mana pots, avoid using the health pot. (healthstone, various healing crystals or trinkets, even bandages are sometimes better substitutes.)
3) Illumination and Divine Illumination - yes, they have cooldowns, but the cooldowns are far shorter than the trash between bosses, and in many cases shorter than the boss fights themselves. Use them. Often. And again. Many healing trinkets also have extra +healing on use. Use them.
4) Don't forget Lay on Hands - Very nice for late in the fight, when all the priests and druids have run out of mana and you're just getting ready to take your next mana pot - free heal for the main tank to full health, then pot and keep going. Again, you may be able to use this two or (with Improved Lay on Hands) three times in a major raid, and at least once in an instance.
5) Don't forget your bubble. Bosses that polymorph everybody, things that do massive instance damage at a known time, even suddenly picking up lots of aggro, this will shed it very quickly leaving you free to focus on healing. Plus, you usually have time once you're free to dispel the effect off of one or two other people.
6) Cleanse - You can mitigate far more damage than you can heal in many cases just by cleansing off debuffs - polymorphs, fears, poisons and many effects that either cause squishies to die fast or cause the tank to run around helpless while the boss beats on the rest of the party can be stripped almost as quickly as they're laid on.
7) Know when to wait. Especially in large raids, there are a lot of situations where everyone in the group tries to heal anybody taking damage, and you end up with lots of overhealing and everybody running out of mana. If two of you are assigned to the same target, you can take turns healing - after 5 seconds of not healing, your mana starts regenning with spirit again. Be ready to jump in if the damage starts overtaking the other healer.
Lol - okay, a few more than a couple. Enjoy!