There are 3 Phases :

Phase 1:
100%-70% of Health

Start the fight by talking to Tirion Foldragon and the event will be triggered
Few seconds after the start of the Fight He will do Infest - Inflicts 6,598 to 7,402 Shadow damage to the entire raid. In addition, affected targets will take increasingly higher Shadow damage every 1 second, starting at 1,000.
Secondary effect is removed when the target is at more than 90% health and during that time also he will

Summon Ghouls and Shambling Horrors
1 of the tanks takes adds facing away from the raid (they do frontal cone for alot of damage) and 1 takes the Lich king.

During Phase 1 The Lich king will also use Necrotic Plague - A disease that inflicts 50,000 Shadow damage every 5 seconds for 15 seconds. If the effect ends (it expires, host dies, or is removed with a spell), the plague will jump to another target. If the effect is removed with a spell, the plague will lose a stack; if the target dies while affected, it will gain a stack. Whenever the plague jumps, the Lich King gains a stack of Plague Siphon. The tactics to overcome this Disease is to move near the adds that are being tanked and healers dispell the debuff of you. It is your NUMBER 1 Priority(stop your casts/dps/whatever and head to the adds)

If everything goes well at 70% the Lich King will run to the middle of the platform, cast Relentless Winter - Inflicts 7,069 to 7,931 Frost damage every second to players within 45 yards and start casting Pain and Suffering- Inflicts 2,828 to 3,172 Shadow damage to enemies in a frontal cone, as well as an additional 500 Shadow damage every 3 seconds, stacking up to 5 times very frequently, so the raid moves to the end of the Platform!

When the raid is at the end of the patform he will create 3x Raging spirits during and some FrostBalls. 1 of the range Dps-ers must handle them while the rest of the raid kills the Raging spirits. Again they must not face the raid - the 5 second silence in the frontal cone will probably wipe somebody. This phase last 60 seconds, and at its end the Lich King will cast Quake, destroying the outermost ring of the platform, leaving your raid with less room to maneuver. Naturally, you should all move in when you see him casting Quake. If you are slower you will fall down and No Ank or Combat Ress will be possible !

When the raid comes back He starts summoning a Val'kyr Shadowguard and it does :
Grab - Grabs a random player and slowly carries them away from the platform. If not killed before she leaves the Frozen Throne, the Val'kyr will drop her target to their death. Everybody should be positoned close to the center of the frozen throne because that will give enough time for the Dps-ers to kill the add.

Finally Phase 3: 40% - 10% :
he will now summon packs of Vile Spirits(The Spirits don't have a lot of health, and should be killed quickly, as they will explode after 30 seconds, doing quite a bit of damage to everyone around them. They are subject to taunts and stuns, so use those wisely.
In addition to the new type of adds, the Lich King will use a new spell as well - Harvest Soul. In the beginning of the phase, he will target a random raider and channel Harvest Soul on them. If the raider survives the damage, their soul will be transferred to Frostmourne. Players trapped inside Frostmourne will see Terenas Menethil fighting against a Spirit Warden. They will need to aid Terenas - either by healing him or attacking the Warden, - so he can defeat the warden and release the player from the runeblade's grasp. Terenas will do more damage as his health goes higher, so healers should only focus on that. The Spirit Warden has a Soul Rip channeled spell, which should be interrupted as soon as possible, as it will damage Terenas badly.

Dropping the Lich King down to 10% ensures that the fight has been won. Watch and listen the cutscene and finish the fight when it is over.

Hope that this helps

Edit: Some misstypes