The First Phase - Taking down the adds
The first phase of this encounter is more or less an add-based fight with an element of mana conservation for your healer. You want your entire party to stay out of melee range of Lord Ahune, including your tank. He hits pretty hard, has a habit of filling your inventory with snow, and like his friends Ragnaros, Murmur, and Thunderaan, he is apparently completely immobile. Ahune reduces all damage he takes by 75% in this first phase, so it is hardly worth trying.
There are a few different types of spawns you will need to deal with during this phase. The first one you will see is the Ahunite Hailstone. This is a large elite frost elemental (though he looks like an earth elemental) that will need to be tanked. For the most part, this is the only thing that must be tanked during the encounter. It has an aura that applies a stacking DoT to those in melee range of it, each application doing an additional 300 damage every three seconds, up to ten applications. That comes to 1,000 DPS from this DoT, so you may want to put only your tank and your ranged DPS on this. Rogues can use Cloak of Shadows to remove it, so they can fight the Hailstone if they really want to do so.
While you are fighting this elite, many non-elite elementals will be spewed forth from Lord Ahune. They have somewhere between 1500 and 3000 health, so they're very easy to kill. Taking these guys out is a good task for your melee DPS if you have enough ranged to bring down the Hailstone without their help. If your ranged DPS is good, you can probably bring down the Hailstone very early, and your entire party can focus on the little guys.
If you have a Warlock, you can have them cast Seed of Corruption on the Hailstone, and that will pretty much take care of all of the non-elites and your entire party can focus on the Hailstone if you're willing to risk the aura. The aura is only a minor threat if your party can focus fire it down fast enough. Most healers can handle that DoT fairly easily if your group is geared well, and the non-elites aren't too dangerous in this first phase as long as they're killed. You don't need a terribly organized strategy for them, just don't let them pile up. They spawn continuously, and if you leave them alive they will probably destroy your healer.
The other thing to watch for in this phase is the spikes of ice that shoot up from the ground at random. They will occasionally spawn beneath someone in your party, and launch them into the air and cause them to take falling damage. You can see the ground swirl and freeze beneath you before they can even hurt you, so there's plenty of time to get out of the way before they hit you.
This phase lasts roughly 90 seconds, and is largely a game of survival as long as you get the Hailstone down early. After 90 seconds, the Earthen Ring shaman trio behind you will have successfully melted away Ahune's defenses, and leave his Frozen Core vulnerable.
The Second Phase - DPS'ing the core
This second phase is straightforward. As long as you have all of the adds down (which you should) there is no more damage being inflicted upon your party at all. Your entire party can, and should, focus damage upon the core. If your healer is having a hard time with mana, they can wand or autoattack and let their natural regen kick in. If they're overgeared for this and have an abundance of mana, let them go wild with Smite/Wrath/Whatever. Burn all of your cooldowns here. If you have a Shaman, Heroism/Bloodlust is amazing. If your group is exceptionally well-geared, you can finish the Core off your first time to Phase 2. However, most groups will not be able to pull that off.
Once again, Warlocks can do something a bit extra here. Since the first phase lasts 90 seconds, you can wait 30-35 seconds and cast Curse of Doom on Ahune himself. It'll explode shortly after the Core is revealed and phase 2 begins, and do a pretty hefty amount of damage.
This vulnerability stage will only last 30 seconds, so hit him as hard as you can. If you get him to 50% your first time seeing the Core, you're more than alright. If you're closer to 75% (or higher than that) you're probably going to find yourself in a tight spot, unless you only did that much damage due to having 2-4 healers in your party. If that's the case, you're just fine. The fight will take you thirty minutes, but you're fine.
Rinse and Repeat
After thirty seconds, we're back to the first phase. Tank the Hailstone as before, but the non-elite adds will be more numerous and varied. This continues each time you need to repeat the first phase. Most groups can survive three visits to this first phase. The fourth one will probably be the death of you. Most groups, however, should not need a third or fourth visit to this phase. As I said, if you can get his Core to at least 50% your first time seeing it, that's perfect.
Once Ahune's Core hits 0, the fight ends and you can watch the fun death animation complete with spinning scythe. Open the chest, distribute your loot, and be on your way!
Resummoning the loot pinata
You can summon Ahune once per person on Normal mode, and once total on Heroic. The fight is more or less identical on both modes. The only noticeable difference is that the Core and the Adds do a little more damage, and have a lot more health. Make sure you empty Ahune's chest when on Normal mode, or the summoning crystal won't respawn for another summon.
Good luck, and have fun! Even if you have no interest in the loot at all, I recommend giving this encounter a shot. It's very, very fun, and something you won't be able to see again for at least another year.