Do you have the gear?
Before you ask, I'm personally recommending you have an ilevel of at least 340. The higher, the better. But don't even set foot inside a raid unless you're with an exceptionally geared group of skilled players. You may not be able to contribute as much as you think.
And make sure you actually augment the stuff you get. At the very least, use green-quality gems. I started using superior gems in my ilevel 333 items. I've found that they made the difference between running out of mana at 15% and running out of mana at 5%. The latter allows you to "coast" to the win and use your spells when you have just enough mana for it.
Seriously, I never understood the stigma of not using enchants or gems on gear. Gear progression is like a stepladder. You can't get to step 3 without going through step 2. You can't get to step 2 without going through step 1. You get all the skill you want, but it has always been my belief that if your gear level isn't at the right spot, nothing you can physically do will help.
Don't be afraid to use enchants or gems as you go. Some of them are fairly cheap. At the very least, consider using stuff from Wrath. I didn't have my helm enchant for the longest time because I hadn't gotten the appropriate reputation from Guardians of Hyjal (Arcanum of Hyjal). So I backtracked and grabbed the one from Wyrmrest Temple (Arcanum of Blissful Mending). It wasn't much, but at least it was something.
I once wiped at 6% on Admiral Ripsnarl. I stretched out the encounter as long as I could, but I just wasn't able to continue healing any further. I used every cooldown, every consumable, and every trick I had up my sleeve. Doing a quick sweep of the players in the group, I noticed they were missing enchants or gems. They refused to waste their money or enchanting mats on gear they were going to replace anyway.
I became extremely upset because had their gear been appropriately enchanted or geared, the Admiral would've been taken down and we could then have moved on. But because of their unwillingness to spend even a bit of money, we couldn't progress. After another attempt, I apologized and dropped group while stating that even though I invested in enchants for my gear, their lack of investment could have easily made the difference between the 6% wipe and a win.
Have you been working on your skills?
Healers received a number of additions to their abilities. I know it took me a while to figure out how to use life grip (or Leap of Faith, as it is more formally known). If you want to get better at healing overall, though, you need to start with heroics. If you don't understand the following basic concepts, then you won't last very long.
Mana matters. Not saying much here. Our spells are expensive, with the exception of a normal healing spell. That's not to say rapidly casting a big heal or a small heal isn't an option either; the trick is to know when. As the health of a heroic boss gradually drops lower and lower, healers have more leeway to use additional expensive spells (assuming mana cooldowns are used). I'm not sure if you've noticed, but there are a number of encounters where bosses just enrage after their health falls to a certain percentage (usually 30%). Don't hesitate to go all out or all in at that phase, because I guarantee you it's almost a necessity.
Full health isn't a necessity. I'm repeating this again just because it's that important. In fact, I think I'm going to try to find a way to repeat it every week until everyone understands how this new healing model works. I'm not ever going to get kicked from a random dungeon again because players don't understand that they're not supposed to be topped off all the time. I'd rather have the distinct pleasure of just leaving the group myself.
Are you eating right?
The last part to success is bringing your consumables. I've upgraded to using Flask of Flowing Water when it comes to progression and learning new raid encounters. Flask of the Draconic Mind is another alternative. For food, I like to dig my fangs into some Delicious Sagefish Tail.
Try to keep a stack of Mythical Mana Potion on you. But I do understand that it can be expensive if you don't have a character who can produce it. These potions run for over 30 gold individually, where I'm from. I've usually been on the fence when it comes to bandages, but I'm going to start carrying a stack of Dense Embersilk Bandages myself. While I could easily use a spell to heal myself, that mana might be better spent on another player. There might even be times on an encounter when I'm the only player who took substantially more damage than someone else (because I stood in a fire longer or something).
Last-minute pro healing tip: Read up on raid encounters early and watch some videos of them. Look for key moments in encounters where you can slow down your healing and use your mana regeneration cooldowns. I've had cases when I used a cooldown a little too early and I never received the full benefit of it because I got knocked in the air, knocked around or experienced something that interrupted my cast bar.
Need advice on working with the healers in your guild? Raid Rx has you covered. Send your questions about raid healing to firstname.lastname@example.org. For less healer-centric raiding advice, visit Ready Check for advanced tactics and advice for the endgame raider.