Gothik hangs out on a balcony overlooking the room. He is targettable up there and the fight starts when someone attacks him. In the middle of the room there is a gate which will close when the fight starts so you have to split your raid in half and try to balance equal amounts of DPS on each side of the gate. The side of the room where you enter is generally referred to as the ‘live’ side and the other side as the ‘dead’ side. On the wall on the left side of the live side there are three platform type things (I don’t know how to describe them but you will know what I am talking about when you see them) that mobs spawn on. The little humans are mostly harmless and have relatively little HP and will be killed pretty quickly – far too quickly for them to kill even the squishiest member of your raid so you really don’t need to worry about tanking them. The mobs that you need to worry about are the Death knights and the Horses and Riders. These have more HP and do enough damage to kill a squishy if they aren’t picked up quickly (although it’s entirely possibly to face tank them with a ret pally, dps warrior or a non-tank DK as long as DPS nukes it down quickly). But even those mobs don’t have a ton of HP and will be dead in less than 15 seconds. At the beginning of the fight only the humans will spawn and they do it rather slowly and as the fight progresses, the bigger meaner mobs start to spawn as well and the pace at which the spawn picks up quite a bit.
Whenever a mob is killed on the live side, its spirit travels over to the dead side and respawns as an undead mob (back in the day the undead mobs were immune to magic damage but I am not sure if that is the case anymore). If you are tanking on the dead side you can watch the spirit traveling over to your side and then moving towards one of the 5 piles of bones on the ground at random. When it gets to the bone pile the new add will spawn on that spot. When one of the little humans on the live side gets killed, an equally ignorable mob spawns on the dead side, when a Death knights or Horses and Riders die on the live side, a Deathknight or Spectral Horse and Spectral Rider spawn on the dead side and just like the live side, these need to be tanked.
After 3:45 the mobs stop spawning and once you finish off the adds or at 4:30, whichever is first, Gothik himself joins the fight by teleporting down from his balcony to the live side of the room. He will chain cast non-interruptible, non-reflectable shadow bolts at the tank and casts a nasty debuff called Harvest Soul. Harvest Soul last 60 seconds and it reduces your stats by 10% and stacks up to 10 times and it hits everyone in the raid. Harvest Soul is basically a soft enrage timer. After a little while on the live side he will teleport over to the dead side and that group gets their turn. Back in the day, he would teleport back and forth a couple time with the gate in the middle closed until you got him down to 25% (I think? Maybe it was 40%) and then the middle gate would open up and everyone could dps him at the same time. The last few times I have been in there on both the 10 and 25 man version, our dps was high enough and his HP is low enough that I can’t really tell if he still goes back and forth a few times or if the gate opens automatically after the first teleport.
This used to be one of the hardest fights in the instance. For as many guilds as got stuck on the Four Horsemen, almost as many were stuck on Gothik. Today you just zerg your way through all the adds and nuke the boss and it really very simple. But at 60 you couldn’t do that at all, the mobs had a lot more HP relative to the raid’s dps so they were harder to kill in the first place, but you also had to strike a balance between killing and CCing mobs. If you killed too many on the live side, then the dead side would be overwhelmed and you would wipe. But if you tried to sheep/shackle/fear too many mobs on the live side, eventually some CC would break and you would start losing people and then live side would get overwhelmed and you would wipe. It was quite a balancing act to have the right CC/DPS combinations and then it had to be executed flawlessly. On the beta, this fight was the hardest one in Naxx and was reportedly very tightly tuned, especially compared to the rest of the instance. It got nerfed a couple times and the version that made it live is pretty mundane.