When help's already on the way
Sniping heals is the act of casting a fast healing spell on a wounded player before someone else's spell lands on them. Generally, this practice is frowned upon, as it makes it appear that the healing meters are being manipulated. It also potentially leads to overhealing. Depending on the gear of the group or the encounter, constant overhealing could lead to low mana as your group progresses through the encounter.
However, there are exceptions. For example, a player may have less than 20% health and you can gauge that a large heal is incoming, but you may see that spell will not land soon enough. There is a risk that the player could die before that happens. By all means, use a Holy Shock, Riptide or some other instant spell to increase the player's health buffer.
By contrast, if a player is around the 70% range and there is an incoming heal, you can peel off and look for other targets who are in need of your heal.
Working around cooldowns
This part of healing takes a little more effort. If your team is taking an extreme beating with the cooldown up, you may need to rely on fast, constant heals just to sustain their health.
If the incoming damage is coming in at a slower rate, slower but stronger heals would be the way to go. Sometimes a few simple HoT spells will be all that's needed to get a tank through the next few seconds. Use your discretion, and try weaving in different abilities. It is an open-ended situation and it will take practice before you can get it right.
If a cooldown is being used that affects the entire raid (Tranquility, as an example), you can breathe a little bit easier. When one of my players uses an ability like that, I specifically look for players who are close to death. One or two fast healing spells is enough to get them out of danger, and then I let Divine Hymn or Tranquility do the rest of the work. Go from player to player and actively identify who is going to drop.
Coping with expected damage
With enemy spells like Blackout, we healers should have an idea of when big damage is about to impact the raid. There are a few things you can do to gear up for it. This tactic could be viewed as partially wasteful; one question I get is what's the point of throwing a Renew on a player if there isn't any damage to heal up yet, right? The effect is that it further adds to my healing done when the raid does eventually get hit. A player who gets healed with a Flash Heal and a Renew is always going to get more health compared to a player who just gets Flash Healed.
Think about global cooldown (or GCD) management for a second. You may not be able to spare the GCDs during those intense healing phases, because you're too busy unloading your large heals. Even if you end up wasting the first tick or second tick of a Renew, the subsequent ticks of it will continue to be effective.
Naturally, whether or not you can do this depends on the mana regeneration of your character. When I first started out, I could only pre-HoT one or two players. Now I can do it to three to four players without completely taxing my mana resources.
Keep key players on their feet
Other than tanks, raids generally have a select few players who have their own unique roles. Sometimes, they are placed in positions where they need extra care; for example, getting targeted by Atramedes during an air phase comes to mind. If I'm on raid healing duty, the job of taking care of these players is also mine.
Keep in mind that the spells you use to heal up special players will depend on the encounter. Getting chased by Atramedes? No problem. Use HoTs and really fast heals until the beam switches off to someone else.
Someone getting floated up in the air during the last phase of Ascendant Council? Hit him with fast heals, and then target anyone else who's also getting floated up. Hopefully, one of the players is already in range of you. While you're unloading instant spells, start moving in the direction of the other players, and cast spells on them once your initial target is clear.
I realized after the first few attempts that the trick was to not go overboard on one player. You don't have to heal them to full. You just have to heal them enough to the point that they can survive simple fall damage.
My point on accessibility refers to things like line of sight and range. In large areas, have the foresight to position yourself where you're not too close to other healers. Unless the encounter demands it, it is pointless to overload one side of the room with healers and next to zero on the other. Do keep spacing issues in mind.
The second aspect of accessibility is to learn to keep your head up and shake away tunnel vision. In the same example above, if you see someone being levitated off the ground, you can immediately start moving in and closing in on them. When I do this, I keep pressing one of my instant spells. If I hear the prompt saying I'm out of range, then I still need to carve a path and move closer. If I don't hear anything, I'm at the right spot.
Above all else, keep practicing. Healing is like chopsticks: easy to pick up, difficult to master!
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.