Also popularly known as pillar-humping, or using the pillars in Arena maps to break or abuse Line-of-Sight, this isn't as simple as sticking to the column in Nagrand. It takes a keen awareness of the map and, more importantly, awareness of your enemy's and teammates' positioning. To help with this, have your team leader place raid symbols on each of your members to make it easier for you to spot your teammates across the Arena map. You should also convert your party into a raid so that the symbols stay through matches. You can toggle 'V' to show enemy health bars, as well, which should give a general idea of where everyone is.
Some opponents bear more watching than others. For example, Priests will always be a threat because of Mana Burn. If a Priest has you targeted and starts to cast Mana Burn -- needless to say you should have the Target of Target display always on -- you can jump behind a pillar to break casting. The same goes for other effects such as Cyclone or Polymorph. What LOS won't break, however, are channeled spells like Drain Mana, so the only way to escape this is to interrupt the caster or run out of range.
Against melee classes, running around a pillar can frustrate opponents as long as you manage to keep snare-free or snare your opponent to the same speed. The health bar will show through the pillar so you'll always be aware of where your opponent is and be able to try and stay directly opposite them. This works for the pillars in Nagrand and the pillars supporting the bridge in Blade's Edge. You can try to circle opponents in Lordaeron, too, although it's easy enough to hop over to the other side.
The top of the crypt in Lordaeron creates a lot of problems because the four posts on the corners break LOS, so healing on top of it can sometimes be difficult if your teammates constantly circle it. This is obviously easier for Druids and Priests who can throw HoTs on their targets to buffer cast time heals, but harder for Shamans and Paladins who must stay still in order to land a heal.
Learn to kite. If their DPS is on you, it's important to kite them. Humping helps a lot, making it easier to escape ranged classes. At any rate, try not to stay static, even if there aren't any opponents on you. Learn to move with your team so that nobody overextends and goes beyond your healing range. Memorize the features of each map, as the different maps have unique structures that aid humping -- the pillars in Nagrand is an obvious one, as is the crypt in Lordaeron. Blade's Edge is an extremely fun map because you can weave through the bridge, the ramp, and even the pillars while you can use the starting areas in Lordaeron to jump out of LOS. The longer you stay out of LOS, the better. Just don't forget to keep your teammates topped up.
Another important skill for healers is faking a heal. This is perhaps more important to Paladins than any other healing class because getting interrupted while casting locks the Paladin out from doing anything at all. For this reason alone I still employ the obsolete /stopcasting macro which cancels my current heal instead of putting it in the queue. This is more efficient than breaking heals with movement, which costs precious split seconds.
It is imperative to get an AddOn that helps you track spell cooldowns, such as the essential Afflicted. This is probably one of my favorite AddOns in PvP, giving me an idea of my window to cast spells. It also helps to understand what classes can interrupt and lock you out of a school. For example, if a Shaman is waiting for my heals I don't worry too much because Earth Shock is a mere 2 second school lockout (GCD is already at 1.5) whereas Pummel, Kick, and Counterspell all have longer lockouts at 4, 5, and what feels-like-forever 8 seconds respectively. There's also the Shadow Priest's Silence and Felhunter's Spell Lock, although Silence is on a 45 second timer and many Warlocks usually, naively, leave Spell Lock on auto-cast.
While humping should probably be your first option to avoid interruption, juking is a close second when the match requires you to be in the thick of things. Some good players will have you set as their Focus, making it easy to Counterspell or otherwise interrupt you even in the middle of DPSing. Juking is essentially the pump fake of PvP and you can throw 1 or 2 fake heals in order to bait an interrupt. Having Afflicted allows you to monitor your window and give you latitude (or courage) to heal like a madman. Because there's so much damage being dealt in Arena matches, it happens often that you'll need to throw out your biggest, longest cast heal so you'll need as much leeway as you can get.
Of course, having a Rogue on you is a different matter altogether as they simply have too many options to completely shut down a healer. From Kick to stuns to Gouge to Blind -- and even an offensive Sap used when you're casting out of combat -- a Rogue can effectively impair healing completely. Although this can gimp their DPS, some teams will take the tradeoff in order to remove a healer from play. In situations like these, the only thing you'll need to watch is Kick, as it's the only spell with a school lockout. You can also trinket your way out of a stun or Blind, so the best thing to do is take it on the chin and hope your teammates can peel the Rogue off your butt.
The last great skill of any Arena healer is the art of drinking. Although this applies to all casters, it's critical for a healer because a healer without mana is equal to a dead teammate. Particularly against teams with drain capabilities, drinking is part of the combat experience. You will, invariably, find yourself out of combat several times during a match. Pay attention. Drink. If nobody is dying, drink. Find a pillar, sit down, and drink. Needless to say, always have several stacks of Star's Tears ready before every match.
This is an extremely difficult task, however, against teams with pet classes. Smart players will have their pets constantly on the healers to keep them in combat, preventing drinking. There's simply nothing you can do against this except to kill the pet or run it across the map as far away from its master to despawn it (I'm not sure this still works). In these situations, call for help. It's your teammates' responsibility to peel at least the pet off you in order for you to find a window to drink.
When should you drink? Personally I'd say early and often. As long as your teammates are in good shape, drink at every opportunity. This means any window where you get out of combat. If you're not the only healer, coordinate with the other healer to buy some time to drink. Mana is not a constantly self-renewing resource like Energy or Rage, so it's important to have as much mana during a match. A mana-less healer is often the target of a swap and is also often very dead.
There you have it. Three simple skills that should help any healer in Arenas. Needless to say it also requires extensive knowledge of your class... a Priest healer won't simply be spamming Flash Heal, for example. It's usually a healer's responsibility to dispel, too, so there's a strategic choice of whether to activate the GCD for a dispel or continue spamming heals. Have a good time keeping your friends up, and always remember to hump, juke, and drink.
Do you enjoy Arenas or want to learn more? Read Blood Sport, WoW Insider's column dedicated purely to Arena PvP. Learn more about the dreaded Cleave team composition or how to go about making (or breaking) a Drain Team. If you're a completely new to Arenas, read our Dummies' guides here and here.