To get to Kologarn, you port through into the Antechamber of Ulduar after XT-002, walk up the stairs in front of you, and BAM, he pops up like a whack-a-mole. He looks like a cross between a water color painting of some Titan god and comic book version of Gandalf*. He's got two arms, one of which the raid will sometimes "kill", but then it will respawn a bit later....so he's like one of those strange starfish that will regenerate legs. Or those lizards. That regenerate their tails. Hm.
Two or three tanks will be front and center, tanking Kologarn where he stands. Kolo puts out a stacking debuff on the tanks that reduces their armor, so they'll be doing a rotation, each taunting when the one before has 2 stacks on them. You should be keeping an eye on which tank has aggro and healing them, while also prehotting the tank who will be taunting next once it gets close to their turn. There will also be an off tank who will pick up adds as they spawn, so make sure you know who that is and keep an eye out for those adds. Killing the right arm will spawn them. These adds will cast Stone Nova which does about 8k damage to anyone within 10 yards. Therefore, no one wants to be near them except for the tank.
So where does everyone else stand? Well, you should all be in a horizontal line facing Kologarn, with healers in the middle of this line (you want to be in range of everyone). This is because he does a eye laser thing that will target one person. If he targets you with his eye lasers, you have to run back towards the gate where you came in, and strafe one way or the other. This way, the laser won't hit anyone else; it will hit the ground behind the line of people. It only lasts for a few seconds, and once it's over you can run back into your spot.
EDIT: A couple great things that help: Face the wall behind you. That's right - face yourself AND your camera towards the back of the room. You won't be able to see the tank, but let's be honest, you never see the tank anyway. You're too busy looking at Grid or Healbot or Xperl or whatever you use. (AMIRITE?! I mean, srsly, Kologarn could be the Kool-Aid man for all I know. I have no idea. I'm too busy watching small boxes and health bars =P) This way you can see the eyebeams to the left and the right of you when they start up, and you can start running WAY before they hit you. It's *awesome*. Seriously, you'll never take damage from them again. The eyebeams take about a second or two to actually meet in the middle (the middle being where you're standing). You'll see them way before they meet, and you can start to run with plenty of time. Note that this totally doesn't work for DPS, for obvious reasons.
Because of this, you CAN'T wait for DBM to tell you that the eyebeams are on you. If you wait that long, you're too late, and they're already damaging you. Keep that in mind, and use visual cues, not just DBM.
Every so often he'll grab a couple players and Stone Grip them in his right hand. DPS have to switch to the right hand and damage it, to the point where he drops them. They'll be taking quite a bit of damage in there, so be sure you know who's been stone-gripped and hot them up.
Kolo's left arm will sometimes do an AoE "shockwave" that will bring everyone in the raid to under half health or so. Yes, it's a bit scary. When this happens, it helps to pop Barkskin and then remember not to panic - just hot everyone up as best you can, throw some Nourishes on them and get everyone back up to full health. Remember to keep your hots on the tank while you focus on the raid, as well. Also remember that you have 5 or 6 other healers that are helping you do the same thing. It will help to give priests assigned groups to use Prayer of Healing during this phase. If you have the mana to do so, I'd keep one LB ticking on a few different people who might have low health in general during the entire encounter, to help get them back up to full as soon as possible once that shockwave hits.
Once you have these mechanics down, it's pretty much just heal heal heal.
*Interestingly, he does yell "None shall pass!" when you aggro him. ^^
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