Welcome to the (often) thankless world of Healing! Brace yourself for the torrent of abuse, blame and self-entitled whining that will be winging it's way to you shortly.
In all seriousness, I consider myself to be a pretty good healer (*smug*smug*) and there are a couple of things to bear in mind:
The Order of Heals
Generally, healing priority goes: Tank > Healer > DPS (that is, Tank gets first dibs, followed by the Healer (i.e. you), followed by the DPS). So if both the Tank and DPS are taking damage, the first heal you cast should be on the Tank, and then the DPS. If only the DPS are being damaged, however (which really shouldn't happen anyway), then obviously you heal them. If you're doing PUGs/non-Guild Groups, then it's important to lay this on the table first thing, before any battles - this helps avoid any confusion/whining about it later on. And if whining does occur, you can tell them that you told them so.
Obviously, depending on your particular play-style, you will have an optimum build for your Healer that may be different from my optimum build. That being said, this is how my Sorc Healer is set up:
Skill Point Allocation: 33 - 7 - 1 (Corruption - Lightning - Madness)
*Corruption (33) - All skill maxed, except Fadeout & Conspiring Force:
Fadeout (4th Tier - 0 points) - Really only helpful for giving immunity to movement impairment, which as a Sorc Healer isn't all that important, since most of your heals can't be cast while moving, and a quick burst of Force Speed is all that's necessary to remove you from harm's way (and you have to use Force Speed in order to get the benefit of the skill).
Conspiring Force (5th Tier - 0 points) - This is a movement impairment effect added to Affliction (which you'll hardly ever use if you're a dedicated Healer anyway) which isn't really all that useful, since Force Slow gives the same effect and also does additional damage.
*Lightning (7) - Points in:
Reserves (1st Tier - 2/2) - Very helpful, especially at lower levels, since it increases your Force pool by 50 points each time - a must-have skill and the first non-Corruption skill to be invested in.
Electric Induction (1st Tier - 3/3) - Maxed out, it reduces the cost of your healing abilities by 9% - very important as it helps conserve your Force pool.
Lightning Barrier (2nd Tier - 2/2) - Not really necessary until the higher levels (around 44/45 when you can't invest in any more Corruption Tree skills other than the two to be left empty) - this increases the amount your Static Barrier absorbs by 10% each time (for a max of 20%) - a very helpful buffer to damage, which should be cast on everyone before a battle/the Tank during a fight.
*Madness (1) - Points in:
Sith Defiance (1st Tier - 1/2) - More of an aside, since it's effect is very minimal (1% decrease in damage taken) and only invested in for lack of another, more useful skill.
The Healing Cycle
Once you've maxed out Force Bending (Corruption - 3rd Tier) and Force Surge (Corruption - 6th Tier), the Healing Cycle becomes your best friend. Basically, maxed out Force Bending means that whenever you cast Resurgence, you gain the effect "Force Bending", which means that the chance of a Critical hit on your next heal increases. This is particularly important with regards to Force Surge.
At 2/2, Force Surge has a 100% chance to grant the effect "Force Surge" when you get a critical hit on Innervate (which becomes almost a certainty with Force Bending, since you get a 25% increased chance to get a crit. on Innervate with it). This Force Surge grants you a "free" (in terms of Force) Consumption, which takes a little of your health in return for replenishing part of your Force pool.
Cast Resurgence on Ally/Self (Target gets an immediate heal + additional heals over the next few seconds & you gain the effect "Force Bending") -> Cast Innervate on Ally/Self (Target gets healed over a few seconds & you gain the effect "Force Surge") - > Cast Consumption (takes part of your health and replenishes your Force pool) -> Repeat
By doing this every 8 seconds (for the Innervate cooldown) you essentially keep maximum Force for the entirety of a fight, whilst also fulfilling your role as a Healer. By using this cycle, supplemented with Static Barrier and other healing abilities, you can keep a huge reserve for any emergency healing required during a fight.
Despite what some people believe, sometimes it just isn't possible to keep everyone alive for the entirety of a fight. When a fight's been botched for any reason, you should firstly try your hardest to get your group out of trouble - Use Cloud Mind to deflect mobs attacking you onto other players, and use Extricate to pull any low-health DPS out of the fray/dump their aggro. If this fails, everyone's health's slowly being whittled down to 0, and it's looking like you won't be able to keep everyone alive - then don't. Stop healing the worst of the DPS - cast your AOE heal if you have it, and toss the odd Resurgence/innervate/Static barrier their way if neither you nor the Tank need topping up, but otherwise hang them out to dry. Yes, it sounds harsh, and the immediate reaction of most players is to decry such an action, but sometimes it's necessary. After all, isn't it better to keep yourself and the Tank alive long enough to whittle down a Boss' last bit of health and complete a fight, than for your entire group to wipe and have to start it all over again?
And the truth of the matter is that you can keep a Tank alive far longer than you can a DPS, which gives you a better chance of killing the Boss and allows your DPS more time to respawn at a med-bot and run back to you to rejoin the fight.
So that's it. Remember: this is only a rough guide, and a good Healer knows their limits and is always learning something new. As long as you learn from your mistakes and make it clear to your Group what you can and can't do (especially concerning Line of Sight) then you should find that you'll get the hang of it in no time.
(Sorry for the thread necromancy, but since the question got subsumed in an AOE heal debate, I figured that I could safely contribute.)