The fight is once again split into three phases - ground, air, and ground again.
During the first ground phase, Onyxia will perform a number of abilities typical for any dragon - frontal Flame Breath and Cleave, Tail Sweep behind her, and Wing Buffet. The last one is different than the traditional wing buffets you might be used to seeing - it affects only players in front of her, hitting them for a fairly high amount of unmitigatable physical damage, and knocking them back. Simply tank Onyxia next to a wall, to avoid accidental Tail Sweeps and Cleaves in the DPS.
Phase 1 will continue until Onyxia's health reaches 65%. At that point she will lift off, ignore all threat, and enter Phase 2. Note that while she is flying, melee cannot hit Onyxia, even if they stand underneath her.
There are two kinds of adds you need to deal with in this phase - Whelps and Lair Guards. The Whelps will spawn in packs of 40 (20 on each side). The first wave will come shortly after the beginning of Phase 2, and every ~90 seconds another wave will hatch. Keep them grouped and AoE them quickly, as they are hard to tank for longer periods of time. The Lair Guards spawn more frequently (a pair every ~30 seconds), but are significantly easier to kill, as long as you assign a few ranged DPS to them. They need to die quickly, as their abilities can be dangerous even for geared tanks.
As far as Onyxia's abilities go, the second phase is the toughest to go through. The occasional Fireballs that splash to nearby targets are not too bad, but the Deep Breath (preceded by raid warning) is enough to decimate a raid. As soon as you see the raid warning, note where Onyxia is facing and run to her side as quickly as possible. If it's absolutely impossible for you to get to her sides, try to strafe to the sides at least.
Phase 3 will begin when Onyxia's health reaches 40%. She will land, regain her abilities from Phase 1, and learn a couple extra. As soon as she lands, and occasionally afterward, Onyxia will send the entire raid running in fear for 3 seconds. She no longer drops aggro between phases, so your tank from Phase 1 should still have her. Tremor Totem and Fear immunities are especially helpful here, since Onyxia's powerful attacks, combined with a tank running in fear, and the lava eruptions all over the room can add up to quite a bit of damage.