There are three phases to this fight. In quick summary, the first phase is a ground phase in which your raid goes up against both Nefarian and the zombie Onyxia. (Also, kite adds.) In the second phase, the room fills with lava, and your raid must stand on three pillars (while killing adds and interrupting stuff). The third phase is another ground phase, during which your tank must kite Nefarian around the room. (You still get to fight adds during this time.)
Phase 1 Your first opponent in phase 1 is Onyxia. Her sides glow with little dots of lightning, which will explode in an Electrical Discharge. You can mitigate the discharge by being directly behind her, since the discharge explodes to either side of the dragon. Shadowflame Breath will do damage to anyone in front of the zombie dragon, as well as repowering the bone warriors.
The adds are Animated Bone Warriors. They are powered by an energy bar that will deplete as they fight during the encounter. When they run out of energy, the bone warriors "die" and fall asleep. If any of the fire touches the Animated Bone Warriors, they will come back to life and resume their attack. You can crowd control the bone warriors to keep them from being a big deal, but they hit so hard that you'll have to avoid getting hit as you kite them around.
The key to the first phase is to burn Onyxia down before the electric attacks become unmanageable. After 30 seconds, Nefarian will join the fight. If Nefarian and Onyxia are too close to one another, they'll do double damage. Every time Nefarian reaches a 10% mark (90%, 80%, and so on), he will hit the entire raid for around 100k damage. Healers should be prepared for this attack.
Phase 1 ends when Onyxia dies.
Phase 2 As soon as the second phase begins, the room will fill up with lava. You will need to stand on what were previously pillars. It helps to evenly distribute the raid group among these pillars. The lavas steadily increase in damage, so you will need to hop on the pillars as soon as possible.
There are Chromatic Prototypes that spawn on each pillar. Their Blast Nova does significant damage, so be prepared to interrupt it; this attack will lead to a raid wipe if you let it go off. While you're fighting the prototypes, Nef will rain down Shadowflame Barrage for significant raid damage, so healers will need to be on the ball.
Phase 2 ends when all prototypes are dead or 3 minutes have passed.
Phase 3 During phase 3, Nefarian lands on the ground again. Do all the things you're accustomed to from the first phase, plus have your main tank kite Nefarian around the edge of the room while the add tanks do their best to keep the bone warriors out of the pink fire that spawns on the ground. Nefarian will shoot missiles of flame at the adds, so this is a "do the best you can" scenario. Adds will need to continue being off-tanked and controlled away from Nefarian.
Ready Check shares all the strategies and inside information you need to take your raiding to the next level. You might also be interested in our strategy guides to Cataclysm's 5-man instances, and for more healer-centric raiding advice, visit Raid Rx.