The encounter starts when you simply step into the room with Sara.
Phase One: Sara's guardians
From the clouds in the room Guardians of Yogg-Saron will spawn at an increasing rate as phase wears on, these have to be picked up by the tanks and DPSed down. To end phase one 9 or 10 Guardians of Yogg-Saron have to be killed next to Sara.
When players touch the clouds in the room a Guardian of Yogg-Saron will spawn from that cloud (pets and totems do not add additional adds), this can lead to a raid wipe. The clouds always follow the same path and can move faster then you think. Because of the orbiting behaviour of these clouds the outer edges of the room are less frequently visited by these clouds making it easier to setup the raid there. A general rule in this part of the encounter is to stop all that you are doing when a cloud comes close and move away from it, 3 seconds DPS / Healing lost in this encounter doesn't matter so much as an extra Guardian of Yogg-Saron.
While they are active the Guardians of Yogg-Saron can cast two spells, Dark Volley which can and should be interrupted and Dominate Mind which can and should be dispelled as soon as possible, as an undispelled Dominate Mind can lead to a raid wipe when the controlled people run through clouds.
Upon death the Guardians of Yogg-Saron will cast Shadow Nova dealing massive AoE damage and therefore no one but the tank (and Sara) should be near it when it dies.
There are several ways to deal with the Guardians of Yogg-Saron in this phase, and raid composition matters a lot when choosing the method of dealing with the Guardians of Yogg-Saron. A melee heavy raid might want to DPS down the Guardians of Yogg-Saron away from Sara and then drag the Guardians of Yogg-Saron down to Sara on Low HP so that the ranged DPS can finish it off. While a ranged heavy raid might opt for DPSing down the Guardians of Yogg-Saron near Sara to speed up the killing process.
Each method has it pros and cons in terms of speed and cloud dodging.
A highly effective method of speeding the encounter up is to touch a cloud at the start of the phase to spawn an extra Guardian of Yogg-Saron as the spawn rate at this point in time it's so high that it can't be dealt with.
In the mean time Sara will be casting her spells throughout phase one, however these are a minor part of the phase.
Phase Two: Tentacles and the Brain
When phase two starts any remaining Guardians of Yogg-Saron from phase one should be killed at a save distance from the raid as soon as possible. They will still cast all their spells from phase one.
Phase Two: Try to get the Guardians of Yogg-Saron remaining down before phase two begins because you will immediately be swarmed by tentacles. If you are using Freya and your sanity gets low the green beams on the sides of the room will restore your sanity. Yogg-Saron's body is invulnerable in this phase.
Crusher Tentacle: Melees hard, has a ton of HP and has an aura that reduces damage done by the raid by 20%, stacks with other crusher tentacles so these must go down fast. Melee-ing these will interrupt their aura but they gain a temporary buff that increases their damage and attack speed when they are hit so this is dangerous if they are being DPS'd.
Corruptor Tentacle: Casts various debuffs, Curse of Doom, Apathy, Draining Poison and Black Plague. Dispellers will need to be on the ball. These are interruptable.
Constrictor Tentacle: These have very little HP and appear underneath random players, grab them and hoist them into the air doing damage every few seconds until killed.
Influence Tentacle: These are only inside Yogg-Saron's visions disguised as figures that fit in with the vision. Hitting them will reflect 60% of your damage back on you.
Sara will hover above Yogg-Saron's main body casting various abilities such as Psychosis, Brain Link and Malady of the Mind as well as Death Ray which is similar to Kologarn's Eye Beam but will instantly kill you on being touched.
60 seconds into phase 2, and then 20 seconds after each brain phase, Yogg-Saron will open portals into his brain (4 on normal, 10 on heroic), assign good melee DPS and one healer to take the portals. Do not take the portal if your sanity is low you will lose sanity the longer you are below. You will see one of three random illusion rooms along with some disguised tentacles and laughing skulls floating around the room. The skulls cast Lunatic Gaze so you must strafe around the room with your back to the skulls at all times. The illusion will shatter once you kill all the tentacles in the room. Melee must then run into the brain room and try to get some DPS on the brain before taking the portal back up. The Brain begins a 60 second induce madness cast when the portals open so the melee must complete their task and get whatever DPS they can on the brain within 60 seconds or they will emerge from Yogg-Saron's mind insane. After four portal phases the spawn rate of Yogg-Saron's tentacles increases to levels completely impossible to keep up with.
Phase 2 ends when the Brain hits 30%. This removes the invulnerability from Yogg-Saron's main body.
Phase Three: This is a burn phase, if you took three portal phases to defeat Yogg-Saron's Brain the 15-minute hard berserk timer on the encounter will become a very constricting factor and you will generally have no more than 5-6 minutes to complete this phase before Yogg-Saron berserks and one shots the entire raid. Yogg-Saron will have 16.5 million HP left on 25-man and 3.3 million HP on 10-man. Tentacles will stop spawning, any up will remain. Faceless Immortal Guardians that hit very hard will spawn very rapidly in this phase. You must pick up and kill the Immortal Guardians while also keeping enough DPS on Yogg-Saron to kill him within 5 minutes. Yogg-Saron will begin to cast Lunatic Gaze in this phase so DPS must be ready to avert their eyes. Yogg-Saron will also heal the faceless ones with empowering shadows. It is recommended to save Bloodlust/Heroism for this phase.
When the raid is not using Thorim it is important to remember that the Immortal Guardians hit for less the lower their HP is. So it is likely still not possible to ignore the Guardians and burn down Yogg-Saron as they hit VERY hard at full HP (25k a swing) and will quickly destroy your tanks. Rather you will still need to burn down the Guardians, but they will not die and Yogg-Saron's empowering shadows will heal them back up requiring you to DPS them down again thus making the 15-minute enrage timer very constricting.