The first tip is on how to tell Festergut apart from Rotface. They use the same (hideous) model and their rooms are the same, and both of them cast spells like Gaseous Pungent Stinky Gastric Blight Bloat, so it can be hard to distinguish them! What I did is realize the Plagueworks bosses are in alphabetical order from left to right: Festergut, Putricide, Rotface. And in my opinion it's best to start with #1 alphabetically, since although Festergut has steep requirements for DPS and survivability, it's technically the easiest fight by far.
So Festergut is a cyclical fight. It wobbles between one extreme, Raid Damage to Make a Tree Druid Flail for Joy, and the other extreme, Tank-Crushing Damage to Make a Paladin Cry. When there is a lot of orange blight on the ground, there is raid damage going around, and everyone needs heals. Shamans and Trees will be going nuts here, but you can help out with shields, PoM's, maybe a Divine Hymn if it gets ugly.
Periodically Festergut inhales some blight, which reduces the raid damage, but supersizes the damage he (it?) does to the main tank. When Festergut inhales three times (you can tell because the floor will be blue again instead of orange (also your main tank may start whimpering)), the damage is particularly insane. At this juncture, you should be in full-tank-spam-heal mode. Shield-Penance-Gheal cycles are recommended. Even if you are assigned as a raid healer, there is no raid damage during this time, so you should help on the tank. Divine Aegis and Inspiration insurance for the win!
The other main mechanic is the gas spores. Ranged players need to spread out overall, to avoid Vile Gas. But when Festergut launches gas spores, they need to collapse to share the debuff. Luckily for me, our guild has all the healers stack on the MT so we can heal uninterrupted, but your guild may have you at range, moving around to coordinate the debuff. Follow their lead; trust me that this is one strain of cooties that you DO want. Unless you enjoy eating the AOE he does after inhaling three times!
The fight repeats from there, with Festergut starting his inhale-cycle over each time. It's not a hard fight to heal, it just has sort of a "minutes of boredom followed by seconds of sheer terror" vibe. The only other mechanic is a tank swap (ICC is basically the Land of Required Tank Swap Mechanics. Blizzard could save developer time by just calling all these spells Yes You Need To Swap Tanks Again). But because of the nature of this one, offtank agro may be high, so you may want to be careful with Pain Suppression.
POWER INFUSION TIME
Festergut has a very short enrage timer, necessitating strong DPS as well as strong tank survivability. It's sort of Patchwerk meets the Hokey Pokey for DPS players. All this means for us is, PI early and often, except for when Heroism is up.
BONUS STRATEGY HAIKU
Festergut's strong, sure,
but what role can this guy play
in the Lich King's plan?