The Gates of Hell, the first wing of the Tomb of Sargeras raid, takes you down to the left side of the Tomb where you can place the Tidestone of Golganneth. Naturally, this means that you're going to be facing Naga allied with the Legion. I don't remember if we explicitly know that they're working for Azshara (the whole Legion/Naga/Old Gods relationship is mysterious) but after one big demon, you're going to fight a Naga brute followed by a gorgon-style Naga lady.
As this is the first week of LFR, I'll confess that these impressions will be sketchy, as you tend to get heroic raiders who can blow through LFR easily on the first couple weeks.
This guy shows up in the first big room and is the gatekeeper boss of the whole raid (on Normal/Heroic/Mythic, he'll still be the first boss.)
Tanking this guy is relatively simple. There's a tank-swap debuff that causes you to deal damage to people nearby, so when you get it, have the other tank taunt and run off to the side.
Periodically, Goroth will summon spikes that come up out of the ground. Don't run your debuff into these, as you'll want them for another ability where he deals big AOE to anyone in line of sight. If you get behind the pillar, it'll absorb the blast.
I think that's it for the LFR version.
This Naga brute is probably a lot more complicated on other difficulties. But for LFR, the main thing tanks should worry about is facing. You want to face him away from the raid until he hits 100 energy, then face him toward it so that his cone attack can be split by everyone.
He puts a bleed on the tank that requires a swap.
Harjatan also summons murloc adds that should be picked up by the free tank (though they seem to be casters, so positioning them is not always possible.) I believe these guys are the ones that leave pools of frost damage on the ground. Harjatan eventually draws these into himself, giving him a frost attack, which seems to temporarily replace his energy-based attack.
Make sure your raid has room to maneuver, and you should be ok.
This is another fight that is probably very complicated at higher difficulties. First off, tanks need to swap once the current tank is targeted (you don't have to wait for the spell to go off) with the debuff. This causes any physical damage they take to hit the raid. The off-tank can then pick up eels who deal only shadow damage.
You want to dodge tornadoes that come through periodically (on LFR there are gaps between them, so you only need to dodge.)
Sassz'ine summons a couple of creatures from the deep as the phases go on. One creature will try to suck people into its maw, so you want to run "against the wind" as it were when that happens. You'll also see a big swath of the room light up with a blue watery trail. Get out of that before a big whale dives across, damaging everyone in the path. Finally, I believe you want to run any murloc adds into the jellyfish adds (though as a tank I don't think you get fixated by them.)
I'll post more when I do this from a DPS perspective and might have a better idea of the fights.