Pursuit of Justice pays off
You're going to be running a lot against Ragnaros, and you won't be getting many Blessed Life procs from his attacks. I recommend swapping to a talent spec that features Pursuit of Justice, as the bonus movement speed will help out in every phase.
Speaking of Blessed Life, it is significantly weaker in Firelands than it was in the previous tier. While you're building your talent spec, let me recommend the Glyph of Holy Wrath and the Glyph of Divine Protection for this encounter. The Glyph of Divine Protection is a no-brainer for surviving the incoming fire damage, while the Glyph of Holy Wrath will come in handy later.
Dodge the fire
The first portion of the Ragnaros encounter is pretty boring for healers. You'll be dodging the occasional Magma Traps he deploys; you just run out of them if he tosses one onto you. One of your DPS classes will be running into the trap and activating it, dealing fire damage to your entire raid. You should slowly start healing everyone up after the blast occurs. Don't waste mana on Divine Light; focus on your cheap heals like Holy Shock, Holy Light, and Word of Glory. The Magma Traps come infrequently, and you'll have plenty of time to heal everyone up before the next one is activated. Just make sure to have everyone's life up to around 75% before giving your trap activator the go-ahead.
Ragnaros will also be sending Lava Waves around the room via his Sulfuras Smash attack. Simply sidestep any Lava Wave you encounter, and make sure you're not standing in the targeting area for Sulfufas Smash. With any common sense, you won't have any problem staying alive in phase 1. Your only other concern should be staying away from Ragnaros' melee range, as he will regularly knock back and interrupt players in his melee range. Your tanks will be switching off tanking duty as their debuff stacks up, so just keep Beacon of Light on one of them and keep them both healed up. Unless there's a miscommunication and one tank's debuff stacks up far too high, neither tank will be in any real danger.
If only we had 8 warlocks
Back in my day, when Ragnaros submerged and the Sons of Flame appeared, we stacked enough warlocks to Banish most of them while we nuked the rest. Unfortunately, Banish doesn't work against these new Sons of Flame. The Sons of Flame will start running toward Sulfuras, ignoring everything around them. If they're allowed to reach Sulfuras, you'll all die. There are only two ways to slow the Sons of Flame: stuns and damage.
We're not good at dealing damage efficiently, but we do have some stuns available. We can use our glyphed Holy Wrath to stun two to three of the Sons of Flame in place, allowing our DPS to burn them down without the Sons advancing. Hammer of Justice can be used to stun whichever Son of Flame happens to be the most dangerous, allowing us to stun nearly 50% of the Sons of Flame. It's up to your DPS players to finish the job by eliminating the adds before they reach the hammer.
Use this easy transition phase to pop Divine Plea or a Potion of Concentration, but only after you've used your stuns first. Your mana should be doing fine at this point, as there's really no serious healing necessary just yet.
Dodge the fire, again
Phase 2 is pretty similar to phase 1, as your only real job is to dodge a lot of fire. Ragnaros still uses his Sulfuras Smash, so keep dodging those waves. Instead of tossing out Magma Traps, Ragnaros will engulf one section of the room in fire for a few seconds. The sections are based on your distance from the boss -- there's the near section, which is closest to him, the middle section, and the far section, which stretches all the way to the room's walls. When the fire is there, don't be there. Engulfing Flames becomes more interesting on heroic mode, as Ragnaros will be constantly engulfing the room, but the normal version is pretty tame as you're only dealing with it around once a minute.
Your primary threat in this phase will be the Molten Seeds that Rag tosses out. He'll put one on top of every raid member's current location, and they deal damage based on your proximity to them. You want to have all of the seeds dropped in one location, and then you run to another location and stack up to heal through the explosions. Talk with your raid to find both your Seed drop spots and your Seed stack spots.
Once the Seeds are planted and you've collapsed into a nice stack, you get to start using some cooldowns. Holy Radiance can deal an amazing amount of healing to counter the Seed damage, while Aura Mastery can reduce the damage you take significantly. Divine Protection is wise to use as well; just make sure you pop it before the Seeds explode. Coordinate with the other healers in your raid to rotate different cooldowns through each Seed phase, as you can't use Aura Mastery for every batch of Seeds.
If your friends manage not to drop any seeds on top of the raid and everyone does their job, the healing here is pretty trivial. Pop Holy Radiance and just use your small heals to get everyone back to full. The Seeds also spawn some small Molten Elemental adds, you can again use Holy Wrath to stun these guys for a few seconds as your DPS classes burn them down.
Have the warlocks shown up yet?
Once Ragnaros goes into his second intermission phase, you'll be playing it much the same as the first. Use your Holy Wrath and Hammer of Justice to help out the raid, and then focus on healing the tank who's handling the new Lava Scions. Hopefully, your DPS will be coordinated enough to knock out the Sons of Flame in time. I always hate wiping to a mistake like a Son of Flame reaching the hammer, as there's nothing you can do to stop it once your stuns are used. If you happen to get marked with Blazing Heat, just run to the edge of the room.
Now the fun starts
The final phase of the Ragnaros encounter (on normal mode, at least) is far more exciting than the previous ones. Ragnaros still uses Sulfuras Smash and Engulfing Flames, so you'll be running from the Lava Waves and fiery ground for a bit longer. By now, you should be seeing the usefulness of Pursuit of Justice, as you're simply doing so much running. To add an even larger incentive, you will be chased by some huge Living Meteors as the final phase progresses.
Ragnaros spawns a Living Meteor every minute or so, and you'll need to avoid them at all costs. They're a guaranteed death for anyone who gets hit by one, so be sure to stay out of their path. They'll focus on one player and pursue them, spinning ever faster. If you hit them with an attack, they get knocked back and they'll fixate on a new random target.
You can use your Judgement and Holy Shock attacks to knock them back, but you don't always want to use those first. Use your Holy Radiance and Divine Protection to activate Speed of Light, and kite them around the back of the room a bit. You want to buy your DPS players enough time to kill the boss, so handling the meteor for as long as possible is awesome. Once it gets too close, use one of your instant attacks to force it to pick a new target.
Eventually, there will be several Living Meteors on the field, and it's your job to keep everyone alive. Again, the raid isn't taking any damage at this point. If someone stands in Engulfing Flames or gets hit by a Living Meteor, they're probably dead. You just need to worry about tossing heals onto the tanks and keeping them alive, but Ragnaros isn't dealing any more damage to them than usual. You need to make yourself useful by distracting the Living Meteors and buying your DPS classes time. You can also use Holy Shock and Judgement to help your melee classes knock the meteors back, since they don't always have readily available ranged attacks. Just keep your cool throughout this phase, and Ragnaros will fall before your raid's might for the second time this decade.
The Light and How to Swing It: Holy helps holy paladins become the powerful healers we're destined to be. Find out just how masterful mastery healing can be, gear up with the latest gear, and learn how to PVP as a holy paladin.