Yogg-Saron

Encounter Details

The encounter has 3 phases. Initially, you encounter Yogg-Saron as "Sara".  In phase 2, you see Yogg-Saron in his true form. He begins phase 2 with a protective shield, so you indirectly damage him by killing off his brain. Phase 3 removes the shield and you can begin to damage Yogg-Saron's body.

Phase 1: Sara and Guardians of Yogg-Saron
For phase 1, you'll want to kill the Guardians of Yogg-Saron on top of Sara, as they explode on death.  You'll need to explode 9 Guardians on top of her to enter phase 2.
 
Sara herself is unattackable, and will cast spells on random targets; both players and Guardians of Yogg-Saron.
 
Make sure to stay away from clouds in this phase unless you want to speed up getting into phase 2; standing in them will spawn another Guardian of Yogg-Saron.
Sara
Sara's Anger
Inflicts 12500 Shadow damage every 3 sec, but increases Physical damage done by 12000. Lasts 12 sec.
Sara's Blessing
Heals a friendly target for 27000 to 33000, but causes 60000 Shadow damage over 20 sec.
Sara's Fervor
Increases a friendly target's damage by 20%, but also increases damage taken by the target by 100%. Lasts 15 sec.
Guardian of Yogg-Saron
Dark Volley
Hurls missiles of dark magic, inflicting 8500 to 11500 Shadow damage and wounding nearby enemies, reducing the effectiveness of any healing by 25% for 10 sec.
Dominate Mind
Dominates the mind of the target, temporarily placing them under Yogg-Saron's control. Also reduces Sanity by 4%.
Shadow Nova
Deals 25000 to 27500 Shadow damage on death to anyone within 15 yards; this includes Sara.
Phase 2: Yogg-Saron's Brain, Tentacles and Sara
Basics
HP: 55 million (Heroic) / 11 million (Normal)
Enrage: 15 minutes
Players also begin this phase at 100% Sanity. During this phase, Yogg-Saron spawns Constrictor Tentacle, Corruptor Tentacle, and Crusher Tentacle that you must deal with up top. He's also protected by a barrier that reduces damage taken substantially, though every 90 seconds he emotes and spawns portals.  These portals lead inside of Yogg-Saron's mind.
 
Once you take a portal into his mind, you'll need to kill off tentacles within one of three possible visions that include skulls casting Lunatic Gaze.  If you're taking damage from Lunatic Gaze, simply turn and face away from the skull to avoid it.  After clearing the vision, you can begin attacking Yogg-Saron's brain.  His brain also begins casting Induce Madness when the portals open -- forcing you to exit his mind prior to the cast finishing, otherwise you'll become mind controlled and cannot be freed from it.
 
If you run out of Sanity, you're mind controlled and the effect cannot be removed. You also cannot be battle resed or use a soulstone when this happens.  As a Shaman, Yogg-Saron may also cause you to use your Ankh ability to resurrect yourself.
 
Sara is also present during this phase, hovering over Yogg-Saron as a valkyrie maiden.  Damage dealt to Yogg-Saron's brain is also dealt to his body, thus you must kill the brain to enter phase 3.
Yogg-Saron's Brain
Induce Madness
Drives all nearby targets insane, reducing Sanity by 100%.  This is cast by his brain.
Sara
Brain Link
Links the brains of two enemy targets. Afflicted targets suffer 3000 Shadow damage and lose 2% Sanity every 1 sec. whenever they are more than 20 yards apart.
Death Ray
Blasts the target with a stream of deadly energy, dealing 20000 Nature damage every 0 sec.  4 beams of Death Ray are cast in a target direction and move around toward players.  If hit, you will be killed instantly.
Malady of the Mind
Inflicts 5000 Shadow damage and causes the enemy target to run in horror for 4 sec, then attempts to jump to another enemy within 10 yds. Also reduces Sanity by 3%.
Psychosis
Inflicts 7500 Shadow damage. Also reduces Sanity by 9%.
Hard Mode
Hard Mode involves not having any keepers assist you.  Additional information is as of yet unknown, though more details will hopefully be shared in the near future.
Phase 3: Yogg-Saron and Faceless Immortal Guardians
Basics
HP: 16.5 million (Heroic) / 3.3 million (Normal)
Enrage: 15 minutes
This phase begins at 30% when you've weakened him via killing his brain.  His total HP is actually 55 million (Heroic) / 3.3 million (Normal), but you'll only need to finish off 16.5 million (Heroic) / 3.3 million (Normal) of that.
 
During this phase a skull floats above Yogg-Saron's head and will cast Lunatic Gaze every 15-20 seconds.  If you're unlucky and start taking damage from the skull, turn your character away quickly and it should stop damaging you.
 
Faceless Immortal Guardians spawn and you must deal with them while also damaging Yogg-Saron.  They begin the fight dealing very high amounts of damage, but each attack against them reduces the damage they do.  Once you take them to 1% health, Thorim kills them off, assuming he's assisting you.  If not, you must tank them.
Abilities
Lunatic Gaze
Looking into the maw of madness unhinges your mind, inflicting 5700 to 6300 Shadow damage and reducing Sanity by 4% every 1 sec. for as long as you are facing the caster.
The Four Keepers
When you free the keepers, they move to the positions you see in the image above. You have the option of receiving assistance from the keepers by speaking to them prior to engaging Yogg-Saron. Listed below are the spells each offer if they assist you.
Freya: Resilience of Nature
Increases all damage done by 10% and healing received from all sources by 20%.
Freya: Sanity Well
Standing in the well brings you back to your senses, regenerating 20% Sanity every 2 sec. Damage done is reduced by 50% while you remain in the well.
Hodir: Fortitude of the Frost
Increases damage done by 10% and reduces damage taken from all sources by 20%.
Hodir: Hodir's Protective Gaze
Allows Hodir to save a friendly target who sustains fatal damage by encasing them in a nearly impenetrable block of ice for up to 12345d.  Hodir must rest after performing this action.
Mimiron: Destabilization Matrix
Channels a beam of titan energy that destabalizes the molecular structure of certain Saronite based creatures, reducing attack speed by 100% and casting speed by 300%. Lasts 30 sec.
Mimiron: Speed of Invention
Increases all damage done by 10% and movement speed by 20%.
Thorim: Fury of the Storm
Increases all damage done by 10% and total health by 20%.
Thorim: Titanic Storm
Channels a storm of titan energy that periodically strikes at enemy targets with bolts of lightning strong enough to destroy weakened immortal creatures.
Comments: The keepers alter the encounter quite substantially; Hard Mode will be very challenging without their assistance.

Videos

Now that you've read up on the encounter, take a moment and watch these videos to see things in action.  Multiple videos are available due to the varying roles classes and specs play in the fight.

Ensidia versus Yogg-Saron - Part 1

Ensidia versus Yogg-Saron - Part 2

vodka versus Yogg-Saron - Part 1

vodka versus Yogg-Saron - Part 2

Premonition versus Yogg-Saron