The early trash in the military quarter can be the death of many of a raider due a nice little ability called Whirlwind that one of the little skeletons does, so remind ranged to stay back. It probably will not kill anyone in 10-mans, but we've lost several in 25-mans due to people getting careless.
The Death Knight Cavaliers, found throughout this quarter also like to cast Strangulate, which by itself is very annoying, but as long as multiple healers aren't silenced this shouldn't be an issue. We never had any deaths due to this, so I don't think they cast it often enough to be more than an nuisance.
Between Instructor Razuvious and Gothik the Harvester are some animated weapons (Unholy Axes, Staves, and Swords) that hit pretty hard due to a lethal combination of Whirlwind (Axe), Arcane Explosion and Polymorph (Staff), and Cleave (Swords). Be sure to cleanse the polymorphed raid members. Healing could be rough depending on the strength of the heal team, but as long as everyone's prepared it shouldn't be too bad. It's generally best to take out the Staves first.
The Instructor fight is probably the most different on 10-man vs. 25-man, and is definitely more forgiving on the former. Generally what will happen on 10-man is that the two tanks will each use an orb to mind control a Death Knight Understudy and the understudies will be the ones that actually tank Razuvious. Only the understudies can tank Razuvious because his Unbalancing Strike can hit for 100k on plate, and there's no way to realistically expect a Naxx-geared tank to survive that, but the understudies have a Bone Barrier ability they can use to protect themselves.
Bone Barrier has a 30 second cooldown though. Since it only lasts 20 seconds, this means that the tanks will juggle Razuvious between the two understudies so one tank will have him while the other tank's Bone Barrier is on cooldown. Even with Bone Barrier up, the understudies will still take enough damage that they will have to be healed.
Sometimes raid frame mods won't display health bars correctly if two targets have identical names, so what I do just to make certain I see the understudies' health is I hit V to bring up visible health bars above everyone's head. I'll Beacon the first understudy to have aggro and generally leave it on him for the duration of the spell. Since the tanks will be switching approximately every 20 seconds it would be extremely expensive to recast that spell every switch. The Beaconed understudy will have aggro back shortly enough.
Though the understudies will be taking the bulk of the damage, Razuvious has two other abilities to watch out for. Jagged Knife targets a random raid member and does 5-6k damage on initial hit, but it's the 2000 damage per second after that you'll want to watch out for. Whoever is hit with the Jagged Knife will likely have to be healed in order to survive it. It reminds me of Moroes's Garrote ability back in Karazhan, in that you'll see a raid member's health steadily tick downward, only less lethal since it only ticks for 5 seconds.
The other ability should only affect the melee, and that is Disrupting Shout. If you or the ranged are being hit by this you are standing too close to him. Generally if the tanks keep him in the middle of his little training area and the casters are standing at the top of the ramp leading into his pit you should be far enough away to cast undisturbed.
When Razuvious is almost dead (around 10%) our raid leader will typically call for a halt on heals for the understudies, because after Razuvious is dead the raid will have to kill the understudies. Unless it's an exceptionally close fight, it probably doesn't matter if the understudies accidentally get additional heals because you say... still had Beacon of Light up (oops), but if you can time it right, it's not a bad idea to let BoL expire in the later portion of the fight. Just keep an eye on the understudies' health so they don't die early.
Gothik the Harvester
Gothik is not one of the harder fights unless the raid is divided unevenly. From a healing perspective there is not much of a difference between being on the "live" side versus the "undead" side other than the amount of healing needed.
For this fight the raid is generally split in half, with one tank on each side of the metal gate. The side the raid enters is the live side and the other side is the undead side. Typically the stronger dps/heal team will be put on the undead side, which is considered the harder of the two, since it's more chaotic and there are more mobs (since the riders, which are one mob on live, will spawn as two mobs on undead).
In this fight waves of mobs come down on the live side, and as they are killed they rise as undead (after a short time delay) on the undead side. With the exception of the riders, they generally don't hit very hard. The biggest issue as a healer may be accidentally pulling aggro by healing just as a fresh wave comes down, but as long as your tank is quick they should be able to pull them off you without much trouble.
On the undead side our tanks typically pick an area in the middle to lay down Death and Decay or Consecrate and ask their half of the raid to stand in it to make sure any mobs will run into it upon aggro. This is more important on the undead side since the spawn area is random (and the fights more hectic), whereas it's always the same on live. Warrior and bear tanks will have to be more aggressive about picking up adds if they're covering undead side.
I was placed on live side for my first run, and it mostly consisted of Beaconing the tank and then healing the raid. Healing was extremely light, with the worst thing to watch out for being the Shadow Mark from the death knights that can end up on anyone in melee range. When the riders come out, they have a Shadow Bolt Volley that hits for 3,800 to 4,200 shadow damage, but only against people with the Shadow Mark on them. Even then it's not really heavy damage (unless you happen to be extremely melee heavy), which is why the live side is pretty easy to heal.
The second time I went I healed undead side. I would Beacon the tank and stay near him (but not directly next to him) since my healing aggro would likely aggro newly spawned adds. There's more raid damage on the undead side with Spectral Trainees casting a mild form of Arcane Explosion, Spectral Death Knights using the ever popular Whirlwind, Spectral Riders exuding Unholy Aura just by being there, and the Spectral Horses using Stomp on those in front of them. If the live side is exceptionally fast at killing their adds it is possible that the undead side will be overwhelmed (which is why the stronger dps/heals need to be on undead).
Additionally the Spectral Riders will use Drain Life on their highest threat target, which should be the tank, but could end up being someone else if the situation is exceptionally chaotic. (I ended up getting it on myself my second run, no doubt due to initial healing aggro.)
Shortly after the final wave of adds arrives, Gothik himself will teleport down and begin fighting on the live side. He doesn't hit terribly hard, but he does a stacking Harvest Soul debuff every 10 seconds that reduces the raid's stats by 10%. Additionally, every 10 seconds he will teleport between the live and undead sides, meaning only half the raid will get to dps him until he is brought down to 30%, at which point the gates will open and both sides can fight him.
In theory Gothik is a dps race to beat him before the stacking debuff builds too high, but in reality he's not a particularly difficult fight as long as the two sides are balanced correctly. During the second phase of the fight only the tank should be taking much damage so it's very easy to heal.
The Four Horsemen
Healing the Four Horseman is going to be different for every raid. What your raid does will probably depend on the number of dedicated healers, how many hybrid dps you have, and even how high the raid's dps is. I'll go over a few different possibilities.
When the fight begins, all four horsemen will run to a corner of the room. There must always be someone in each corner with a horseman otherwise the entire raid will be hit with massive damage that is impossible to heal through (ex: Sir Zeliek casts Condemnation if no one is with him). Because of this the raid will always be split up. How they are split up is what depends on raid composition.
Consistent across all strategies is that the raid will have to repeatedly switch targets due to a stacking Mark debuff that is unique to each horseman (ex: Mark of Rivendare). The first Mark will do no damage, but the second will do 500, the third 1500, the fourth 4000, the fifth 12,500, and the numbers only get bigger from there. Generally you don't want to get more than four stacks on you, three to be on the safe side.
As a general rule, Thane Korth'azz and Baron Rivendare must be tanked by real tanks. Lady Blaumeux and Sir Zeliek, located in the rear of the room, can be "tanked" (since they only do magic damage) by anyone. Ideally, given the number of people in a 10-man raid, these last two will be tanked by dps hybrids who are capable of healing themselves, but if there is a third healer that is not needed with the bulk of the raid, it's just as possible for them to tank.
If tanking Blaumeux or Zeliek, all you need to do is stand in their corner and make sure you stay alive. Blaumeux will create nasty void zoids at your feet that you'll have to step out of, but otherwise she's not hard. Zeliek has no tricks at all (though he has a chain Holy Wrath attack that is awful on 25-man).
When you get three stacks of their Mark debuff, switch with the other person who is tanking. So if you start on Blaumeux, let your fellow tank on Zeliek know it's time to swap and the two of you will trade places so that there is always someone in the horsemen's corners. There is a brief grace period where the two of you can be in the middle of a transition and the raid will still be okay.
If you're in the back, it's not a bad idea to throw a Holy Shock on the other tank as you switch places to help keep them up (since they're probably a dps hybrid).
As a 25-man note, we generally pair someone with a lot of health (like a third tank or a feral druid) with a real healer to tank each of the rear horsemen, but in 25-mans there are healers to spare for this.
If you're not placed in the back, then you'll be healing one of the two tanks in the front.
If the raid's dps is not high, then what will happen is the two tanks will switch with each other. When they get three or four stacks of their respective horseman's Mark, the Korth'azz tank and the Rivendare tank will run to each other and taunt off each other, thereby switching targets, and they will run into the respective corner of their new target.
Anyone who was dps-ing Korth'azz or healing his tank will move with their tank into the Rivendare corner and vice versa for the people formerly on Rivendare. My guild generally clumps all the dps on Korth'azz to start with, but some guilds split theirs. In either case, everyone must switch corners to allow time for the Mark to wear off. As always, it's a good idea to Holy Shock someone along the way while you're moving.
If someone stops at the halfway point they may still be in range to get an additional mark from their last horseman and given how much damage these marks stack to, that would be bad, so make sure everyone clusters into their new corner.
If you're healing a group, then I would Beacon the tank so that it's possible to heal everyone else while keeping the tank topped off. If you're healing only yourself and the tank (say the two of you are on Rivendare and the bulk of the raid is on Korth'azz) then I would Beacon myself and then heal the tank. The reason for that is because Beacon doesn't count overheals and the tank is going to be taking more damage than I will be. So it's better for me to get copies of heals on him than him getting heals on me.
The variant that my guild does now that we have more dps is just focus fire Korth'azz until he dies instead of doing the swap between him and Rivendare. Since we bring non-raiders with us we have gotten has high as five marks before, which can be pretty scary, but if most of the raid consists of Naxx vets Korth'azz should go down by the third or fourth mark.
I was put on healing the Rivendare tank, so once Korth'azz is dead and the Korth'azz group comes to take over Rivendare, my tank and I head up to Zeliek. Once we have four marks of Zeliek we go to Blaumeux. By this time Rivendare should be dead and the entire raid will bounce back and forth between Blaumeux and Zeliek until both are dead.
While in the back I'll keep the Beacon on the tank and just heal the raid. If the raid makes it this far, the rest of the fight is cake.
Healing 10-man Naxx Overview - Part 4 - Construct Quarter
Healing 10-man Naxx Overview - Part 5 - Sapphiron and Kel'Thuzad
Healing 10-man Naxx Overview - Part 1 - Arachnid Quarter
Healing 10-man Naxx Overview - Part 2 - Plague Quarter