This is not a post about dual-boxing to fill out your raid, I'm afraid. I know I just lost the huge dual-boxing audience, but I will never lie to you to generate more readers. That's just not how I roll.
This post regards having several characters who heal that you play semi-often. It can be a tricky situation because most healers build up instinct and muscle memory to deal with both having large and diverse toolboxes and yet having to make decisions constantly in a split-second. Oddly, you can't think as you heal...that's too slow.* You need to work instinctively.
*Let me re-phrase that: you can't think in a micro manner, spending time deciding on your next heal. You should be thinking in a macro manner...big picture thoughts about how the fight is going, when you'll need to employ cooldowns, possible strategic changes, etc. Maybe I'll write an actual post about thinking while healing.
So how do you handle switching classes as a healer when instinct and muscle memory are so important? Let's talk about that!
Fundamentally, healing really is the same, no matter what class you are using (outside of blood death knights...they're a freak of their own category). Blizzard has done a good job of making healing classes feel unique (in my opinion, there are definitely those who would argue otherwise) but we can break healing down into certain categories to establish a pattern that we can employ no matter what class we are on.
One major change Blizzard instituted going into Cataclysm was the creation of a set of core heals that, with occasional tiny differences, were constant between all classes. Every class has:
The slow, small, efficient heal: This is Heal for priests, Holy Light for paladins, Healing Wave for shamans and Nourish for druids.
The slow, big, mildly efficient heal: This is Greater Heal for priests, Divine Light for paladins, Greater Healing Wave for shamans and Healing Touch for druids.
The fast, somewhat big, not at all efficient heal: This is Flash Heal for priests, Flash of Light for paladins, Healing Surge for shamans and Regrowth for druids.
This is where you should start, where you should ground yourself, as a healer. Get completely familiar and comfortable with these three heals. Try healing a dungeon using only those heals. Everything else you do should work as an outgrowth from these three heals.
I think this is key whether you have one healer or four different healers, but really making these three heals instinct will make healing over multiple classes much easier. Even if you have just one healer and wish to master it, these three heals are the essence of "triage"--doing only what is necessary (keeping everyone alive), not what would be nice (keeping everyone at full health). Having an automatic feel for when you have to use each heal will simply make you a stronger healer.
Returning, though, to playing multiple healers; consider reserving the same buttons on your mouse (if you are a click-healer as I think most healers are) or reserving the same keybinds (if you use your keyboard to cast healing spells) for these three types of heals. For example, I bind the efficient heal to my middle mouse button, the big, less efficient heal to shift-middle mouse button and the fast, inefficient heal to control-middle mouse button. Whether I am on my priest, paladin, druid or shaman, that's the layout for the core heals. I'm not suggesting you use the same buttons I do, but consider using the same ones between classes for those three heals.
Use On Cooldown
Every healing class has certain spells, usually instants, that are supposed to be "used on cooldown," meaning use it every time it's available. (This is only meant to be literal in raids, when there's always some damage, or difficult situations in dungeons...don't cast them when everyone's at 100% and killing critters while the tank is AFK!)
As a priest, for example, we have two of these spells: prayer of mending and either penance (if the priest is discipline) or circle of healing (if the priest is holy). A druid has switfmend and wild growth. Etcetera, etcetera. While the "use every single time it is up" is extreme in order to make a point (use it a lot!), I'm not arguing usage patterns here...sometimes you may want to hold back a swiftmend for a burst of damage you know is coming, for example. What I'm saying is that every healing class has a couple of spells meant to be used about as much as possible. Unlike the core heals, they are largely without drawback (they tend to instant, pretty efficient and make a difference) and so you use them guilt-free and with abandon. Identify these spells for your class and bind them to the same (hopefully the easiest to hit) buttons.
Every video game has special attacks and WoW is no exceptions. For healers, these special attacks tend to heal people and be rather different. Holy Radiance is fairly different from Power Word: Shield is fairly different from Chain Heal. There is not a lot pulling these things together, in terms of a unifying logic...they are simply the extra moves you can and should use. Ideally, bind them to mouse buttons by binding the most used ability to the easiest-to-hit remaining button, etc.
Binding It All Together (i.e The Big Finish)
The idea that I'm putting forth in this post is to create a "healing logic." Rather than thinking in terms of actual spells, think in terms of a logic or concepts: "Time for my slower, efficient spell. Now my direct heal cooldown. Now my fast, inefficient heal." If you do that, and you bind concepts to buttons, it doesn't matter what healer you're using, outside of the special attacks. Your slow, big heal is always in the same place. Your Always-Use A ability and Always-Use B ability are always in the same place. Suddenly, you can port the same instincts over from healer to healer.
You do still need to change mindsets a little, so you don't Power Word: Shield the rogue (who currently has no aggro) when you were thinking of Chain Heal. But a lot of what you do simply transfers.
I mean, in the end, we're all just tapping into the Great Healing Delicious. We call those methods of tapping it different things and argue over who's Great Healing Delicious is the true Great Healing Delicious...but we're really all seeking the same truth. So bind accordingly!