Healers have been put into a tough spot in Cataclysm. While tanks have an equally stressful job, they are also usually invested with the implicit leadership that allows them to dictate how pulls should be done to maximize their comfort. Healers have a stressful, difficult job and basically have to go along with how the group chooses to proceed. Unless you're a confrontational, take-charge kind of punk...but if you were, you'd have rolled a tank.
So how to handle running dungeons with four strangers who's lives are in your hands? Here are a set of tenets that will hopefully ease your struggle just a bit.
Most groups want to move quickly. Cataclysm was supposed to change people's perceptions of the expected pacing of dungeons because they are, you know, significantly harder than the ones people became used to in Wrath of the Lich King (especially in the final couple of tiers of the expansion, when most people hugely overgeared them).
It hasn't, by and large. Unless you explicitly stop the group, tanks keep moving. Many people are already viewing heroics as the quick, boring and easy task they were back when people were looking for their daily frost. They're not happy with stoppages, even though many pulls can be really brutal on the healer's mana. (This is not to paint everyone with the same brush...there are plenty of sensible, reasonable people...but you don't need these tips when you're lucky enough to group with such people.)
You can always ramp up throughput at need by leaning more heavily on your less mana efficient spells. But for your best PUG heroic results, protect your mana pool. Eat spirit buff food, try to have spirit on all your gear (reforge something to spirit on those pieces that don't) and use spirit enchants/gems. Until mana feels like it's always high, spirit is your best stat (this will change for raids, but we're talking about making heroics easier).
Prepare For The Worst
Define in your mind the worst thing the group can do that you'll tolerate, some combination of not marking pulls, not CC'ing, overpulling, etc. It's a good idea to have in your mind some sense of what the worst you'll put up with is. Once you have that, assume that that is what is going to unfold and be ready to handle it. If the group goes beyond that, drop party. It's as simple as that.
Mind you, I would never advocate dropping party on a group that is honestly striving and has some idea of how to play in instances. Sometimes group composition is not ideal or gear is not high or people are just struggling with a specific mechanic despite generally being decent players. You should try your best to help them succeed.
I'm talking about groups where people really aren't trying very hard and want you to enable their bad play. There is no duty upon you to do so. As a courtesy, you may want to voice your concerns and see if they respond by doing the right things from then on. But dropping party is a perfectly valid response to groups intent on making a mess. It doesn't require being a hardcore player to understand the mechanics of fights, to CC and attack a pull efficiently. It doesn't involve elitism to drop people who aren't interested in putting out that minimal effort when doing heroics.
The main thing is that you have to understand that the responsibility for a successful run does not lie entirely upon your shoulders. In fact, there may be nothing you can do to make a group successful. For your own sanity and enjoyment of the game, develop a sense for those times and cut your losses.
It's Okay If People Die
People die. It's the way of things, in game and out of game. In game, though, the consequences are pretty minimal. Try to save people, but if a DPS has to die, so be it. Don't place the pressure on yourself that deaths represent failures. Success is killing every mob in the pull or killing the boss. Nothing else. If a mage and a rogue die, but the boss dies as well, you were successful. As a group and as a healer. The mage and rogue may or may not berate you, but that's because no one enjoys dying, not because you actually failed (regardless of what they say).
Sometimes you have to make cold, rational decisions and let someone die. Either because there's a more pressing target to heal (the tank, yourself, the one DPS carrying the load in getting the boss down) or because you're low on mana and keeping that person alive is not going to be worth the mana it will take. Steel yourself to make those calls and then make them decisively. Don't waste mana on someone you're going to end up letting die (or who's going to die regardless of what you do).
Don't Be Afraid Of Your Expensive Spells
Blizzard has tried to deincentivize you from using your quick and/or powerful healing spells, because if you used them all the time, healing would be easy. But you are still supposed to use them. I know I told you to protect your mana pool earlier, but a wipe slows the group down more than drinking. Sometimes, you need a burst of healing to save the tank or to stabilize a disaster situation. If things turn grim, pull out the big guns and blaze away. Try to turn them off at the earliest moment you can, though, because you also don't want to run totally dry on mana.
Conserving mana is not an important goal in and of itself. You conserve mana in order to have enough of it when you need to go big. When that times comes, don't hesitate to use whatever you have to.
Remember Your Cooldowns
An easy trap to fall into is to think about your cooldowns as emergency buttons to be saved until you really, really, really need them. The end result, though, is that you'll almost never use them and they'll be wasted. Except in a very few cases, the situation can always plausibly get worse. Maybe a mob will unleash a massive area of effect spell in a few seconds and then you'll really wish you still had that cooldown, right? That sort of thinking is a mistake and paralyzes you from using some of your most powerful spells.
Use your cooldowns at almost any time that you're pretty sure they won't get wasted unless you have an encounter planned out. If there's a specific phase where a cooldown will be maximized, by all means save it for then. But if you're doing a trash pull and lots of damage is happening...start burning those two- and three-minute cooldowns (and fire off 30-second cooldowns essentially any time you can). They'll be back up soon...by sometime in the next pull or even later in that fight if you're attacking a boss. You'll maximize your performance by using those cooldowns as much as you can; waiting for the "perfect time" (again, unless you're scripting an encounter with discrete and predictable phases) will almost always lead to sub-optimal cooldown usage.
Cooldowns are there to be used, not to be saved. They aren't panic buttons, they are powerful spells that Blizzard doesn't want you using too much. Don't increase their cooldowns by using them infrequently.
Take Responsibility For Your Errors
You are as likely to make a mistake as anyone else. It happens. There are a lot of mechanics being thrown around most heroic dungeons, sometimes you'll move the wrong way and bang. Dead healer. Or dead tank. If you know you made a mistake, consider tossing a "My mistake, I missed X" into party chat while running back. It amps down any possible tension, people are generally a little more willing to forgive someone who admits they messed up and it gives you credibility. Credibility is important, for those times when you get blamed and it wasn't clearly your fault. If you've already created a track history of admitting an error, you have a much stronger stand from which to disclaim responsibility when you don't believe it was your fault.
Of course, sometimes you'll have jerks in the group who aren't fair-minded or reasonable and they'll abuse you no matter what you say. In that case, don't bother even getting into it with them. Ignore them for as long as you can, leave the party if it becomes too much to be worth it.
In the end, heroics were designed to be stressful. The LFD tool is there for anyone who wants to quickly find people to run with, but it's not there with the intent of guaranteeing an enjoyable run. For that, you'll need to round up some of your friends. These tips aren't meant to min-max your performance, just to make your heroic runs with strangers slightly less painful. Even the tips aimed at performance (stacking spirit, using your expensive spells, using cooldowns) are offered to reduce the pressure, whether social pressure or decision-making pressure.
Healing is fun, but strangers often aren't. This guide is simply aimed at trying to reduce the potential negative effects of strangers and push dungeon experiences more toward the fun of healing.