Here's the good news: if your co-tank dies and cannot be battle-rezed in phase 3, it's ok! You can solo tank it.
This LFR wing is short and sweet - there's no trash, so you just readycheck and go.
Gul'dan has three phases. He's using the Nightwell in an attempt to use Illidan's body as a vessel for Sargeras, but thankfully the Nightwell (presumably thanks to Elisande's ghost/echo helping you out) will grant players abilities that help with the fight.
Tanks get a couple-second total immunity that takes something like a minute to recharge. You'll want to save this for key abilities.
I believe DPS gets a damage buff that will remain as long as you don't take fire damage.
On phase one, Gul'dan is unattackable, but he'll summon three mini-bosses.
One is a felguard that has a nasty attack that will kill you if you're not using your extra action button (though on LFR you might be able to just use a 50% damage reduction cooldown.)
One is an Inquisitor that doesn't need to be tanked.
One is a Jailor that will throw down soul prisons that all raid members need to run from.
With all the minibosses dead, you move on to phase 2.
During this phase, there will be eye adds that don't need to be tanked. The tanks should stack right on top of each other to prevent his Fel Scythe from powering up. Occasionally the current tank will be knocked back and hit with a snare. You need to run far enough away from your impact point to break the snare, but doing so also does a ton of damage to you - so you use your extra action button.
The other tank should taunt when this happens and then you should stack up again.
On phase 3, you want to pull Gul'dan to one end of the platform. He'll do some nasty damage to you (I think he still does Fel Scythe, but at least on LFR I was able to solo-tank him.) The eyes will keep coming, but as a tank you don't need to worry too much about that.
The key thing is that Gul'dan will occasionally cast a massive AoE that radiates out from him. You want to run as fast as you can to the other side of the platform to avoid getting hit by it (it's centered on him, which is why you always want him close to the edge in this phase.
And for a tank in LFR, that seems to be about it. It's a fun fight that will actually see your health bar dropping.
Now, here's a big tip: LEARN FROM MY MISTAKE: when you turn in the quest to Khadgar (assuming you did the 7.1 Suramar quests) he'll ask you to help teleport the eyes of Aman'thul to Dalaran. DO THIS BEFORE YOU LEAVE.
(EDIT: A note on Fel Scythe:
Because the first week I didn't have a co-tank for much of the fight, I didn't have a great sense of this ability.
Gul'dan gradually builds up energy. If there's a player within 2 yards of the tank, he'll expend all of it and do Fel Scythe, hitting both of them. This also stacks up a buff that increases the damage of Fel Scythe. This stacks up to 10 and hits very hard at that level (probably fatal damage if you're not on LFR.) If he hits full energy, I believe he instantly hits 10 stacks.
So what you do is that while you're not tanking the boss, you step in and let him Fel Scythe once, then step away from the other tank and let his buff fall off (it only lasts a few seconds.) As soon as it falls of, you step in again to make him Fel Scythe. This way he's always casting it at minimum energy and never getting more than one stack of the buff (and if it falls off without getting refreshed, the buff is moot.) So tanks are going to be doing a little hokey-pokey dance with each other over the course of the fight.)
Also, despite only being the first raid tier's boss, Gul'dan gets a cinematic. Spoilers to follow:
Gul'dan watches as the portal into the Nether (red rather than green, which is a little extra scary) collapses. As he sits there, defeated, the crystal tomb of Illidan crashes to the ground. And suddenly demonic wings unfold behind Gul'dan. He turns around, and Illidan is standing there, alive again.
Illidan grabs Gul'dan by the neck, and exactly the same way that Gul'dan killed Varian, Illidan pumps fel fire through Gul'dan until his body explodes, leaving only a skull.
Which Illidan then crushes (no super-powerful artifact this time!)
Illidan then invites the heroes to follow him... into the Abyss!