Strategy

Phase 1
On the pull, bring the Lich King back towards the outer circle, away from the stairs. Melee DPSs from behind the boss in normal fashion, while the ranged and healers should stand to the side leaving the center of the room open.
Infest will deal constant raid damage throughout the fight, and as it and most damage are shadow or frost, Shadow and Frost Resistance Auras are recommended. Infest is a DoT that increases in damage every second until the target is healed to over 90%. The longer it is left up the harder it will be to get everyone over 90% to clear it, so healers need to be quick to get people up whenever the Lich King cast this.

Approximately 15 seconds into the fight the Lich King will summon a Shambling Horror. The offtank needs to pull it to the center of the platform facing away from the raid. The Shambling Horror has 2 abilites, Shockwave, a frontal cone ability and Enrage, which needs to be dispelled by a rogue or hunter.
Also throughout Phase 1, a player will get the disease Necrotic Plague which deals 50k(100k in 25) damage after 5 seconds. This player must run to the OTs position and be cleansed. The cleansed Plague will jump to either the OT or the Shambling Horror. If it jumps to the OT, wait until the person who brought in the debuff has moved away and cleanse the OT so that the Plague jumps to the Shambling Horror. As more Shambling Horrors join the fight (1 every minute) the Plague will spread from one to the next as they die, increasing in damage. If it jumps back to the OT, cleanse him again to return it to a Shambling Horror. If the only Shambling Horror up dies and the OT gets cleansed, the Lich King will cast it on another player and the process starts over.

Also in Phase 1, the Lich King will summon Drudge Ghouls 3 at a time. The main tank should pick these up and they should be burnt down with cleave damage and incidental AoE. Actually, the Necrotic Plague can jump to the Drudge Ghouls as well, so these should be tanked by the OT also so that the plague will jump to them and gain stacks. Eventually at 6-7 stacks the Necrotic Plague will be doing 300-400k per tick (in 10 man at least).

The first phase transition takes place when the Lich King reaches 70%, so try to time that with the last of the Adds going down. Once he reaches 70%, everyone needs to move quickly to the outside of the platform, as the Lich King is running to the center of the platform. Ranged/Healers should spread out and DPS should work on finishing off any remaining adds.

Phase Transition
The Lich King will begin channeling the spell Remorseless Winter and will also cast Pain and Suffering at a random player. Pain and Suffering is a conal ability that deals damage and leaves a stacking DoT, so everyone spreading out will help to keep the amount of stacks/damage down.

Also throughout this phase the Lich King will summon Ice Spheres. The Ice Spheres will target a random player and begin moving towards them. Once they target a player a blue beam will point at the player they will cast Ice Pulse on the player, dealing damage to anyone within 5 yards, which is more reason to stay spread out. If the Ice Sphere reaches its target it will explode, dealing damage and knocking anyone within 10 yards back, and probably off the platform. The Ice Spheres have very little life and a ranged or two should be tasked with killing them before they reach the group.
Lastly, throught this phase, random party members will be targeted with Summon Raging Spirit, which will make a ghosted copy of the character. The tanks should pick these up and face them away from the raid, as they have a conal Damage/Silence ability. Any DPS not killing Spheres should help burn these Down.

After 60 Seconds, this phase ends and everyone should quickly move back onto the main platform as the Lich King will begin casting Quake, which destroys the outer portion of the platform.

Phase 2
Once Quake has finished, Phase 2 begins. During this phase, the Lich King still uses Infest. He also begins to use Soul Reaper on the tank, which deals initial damage followed by 50k shadow damage 5 seconds later. The Tanks should taunt back and forth after getting hit with Soul Reaper so that 5 seconds later the tank does not take a melee hit and the 50k damage at the same time. The raid should position similar to Phase 1, however the Ranged should stay spread as much as possible.

Also in Phase 2 the Lich King will begin to cast Defile. He will target a random player and it is a 1.5 second cast. At the end of the cast, a black pool will appear under the targeted player. Every second the pool will deal damage and for every time it deals damage to a player, it grows in size, so 3+ players getting caught can cause the pool to quickly grow faster than they can get out, ending up in the pool growing over the entire platform wiping the raid. Players should be aware of when the Lich King is targeting them with this ability and be ready to move. The Defile pool last for 30 seconds.

Throughout Phase 2 the Lich King will summon Val'kyr Shadowguards (1 at a time in 10, 3 at a time in 25) who will take about 5 seconds picking a target and then will fly over and pick them up and then slowly begin to fly towards the edge of the platform. If they reach the edge they will throw the player off, so they need to be burnt down quickly. Due to Defile taking up portions of the platform, ranged are probably preferred for burning these down.
These are immune to snares, and already move quite slow, but they can be stunned so if you OT has stun abilities they should move to stun these.
These are immune to snares, however, slowing effects like Chains of Ice and Hamstring will further reduce their movement speed. They are also stunnable, so any available stuns should be used to allow your DPS as much time as needed to burn them down. In 25 man it is advisable to split your DPS up into assigned groups and have them split up on the different Valkyr.

Phase 2 continues until the Lich King is at 40%, at which time he goes into another Transition Phase. The raid should move to the edge of the available platform and the first pulse of Remorseless Winter will reapply the extended platform. The Raging Spirits spawn a little more frequently in this phase so DPS needs to be quick to burn them down.

Phase 3
Phase 3 begins once the Lich King again cast Quake so everyone should move back in. During this phase he will again cast Infest, Defile, and Soul Reaper. Along with these he will now cast Harvest Soul, which will deal shadow damage every second for 6 seconds and if the player lives through this they will be absorbed by Frostmourne.
The other new ability for this phase is Summon Vile Spirits, which will summon 10 Vile Spirits floating in the air above the Lich King. The will remain there for 30 seconds during which ranged need to burn as many down as possible. Ground targeted AoE does not seem to affect them, but abilities like Mind Sear, Seed of Corruption, and DK Diseases do seem to work. After the 30 seconds, any Spirits left will target a random player and charge towards them, exploding for ~15k damage upon reaching them. Ranged should stay spread out and it may be a good idea for melee to spread out once the 30 seconds is about up so that 2+ people standing next to each other don't get targeted.

I am not very clear on what happens inside of Frostmourne but players are apparently able to free themselves somehow.Players sent into Frostmourne must help Terenas Menethil kill an add at which time they are freed.

This phase continues until the Lich King is at 10%...

Phase 4
This I will leave a surprise.