Arcurion himself is pretty basic. His biggest annoyance is the whole Chains of Frost thing. You can't really avoid them, though, so you just have to hope your healer is paying attention and dispels them off you. Hand of Frost, on the other hand, can be interrupted, and your healer will thank you if you do it. Arcurion casts it pretty often, though, so you may want to organize an interrupt rotation with others. Otherwise, try to pull him away from the runes on the ground, as those mark where boulders will fall and cause decent damage to anyone hit by them.
Thrall will eventually be entombed in ice. DPSers, you will probably want to peel away from the boss for a couple of seconds to go help free him, unless the other DPS is ranged and has agreed beforehand to do it instead.
Acurion drops a few good death knight pieces. Iceward Cloak has mastery and parry rating, making it just about perfectly itemized for a death knight tank. Similarly, Arcurion Legguards have haste and mastery, making them very well itemized for death knight DPS.
As a tank, it's generally your duty to set the pace and keep stuff going, so I am going to remind you talk to Thrall before you mount up and ride to Asira Dawnslayer's position. He's only in Ghost Wolf form and will thus be lagging behind as it is, so you don't want to have to run back and talk to him. Once he's there, he'll start into the Quarry. You'll face a bunch of trash packs, most of which will include at least one shadow priest and one hunter.
Kill the shadow priests first and interrupt their spells if you can (Hungering Shadows is the worst), and for extra points, Death Grip the hunter mob back to you when he Disengages. Thrall will lay down totems that give a nice buff if you're in them. If you can, drag the trash into them. If not, hopefully your ranged DPS will at least take advantage.
Asira herself isn't too difficult for death knights. The big thing you'll want to remember as a tank is to drag her out of smoke clouds ASAP and (if possible) into Thrall's totem circles. Of course, sometimes the two overlap, which is a bummer, but what you gonna do? She does have two things that can trip you up otherwise. First, she has Throw Knife, which can silence casters; I have heard rumors that the knives can be blocked by standing in front of them, so if possible, stay between Asira and your healer. Finally, at low health, she'll put up a Blade Barrier that can only be removed by a high-damage hit. You may want to consider saving a strength-boosting cooldown for that, just in case, but it probably won't be a huge deal.
Asira doesn't actually drop anything specifically enticing for death knights, so consider her a bump in the road on the way to the final boss.
Continuing the trend of major Alliance faction leaders and lore figures going insane and trying to destroy the world in the Cataclysm expansion, we have Archbishop Benedictus as the last boss. The trash leading up from him will emerge in small groups from the big black clouds of smoke you see to the sides as Thrall runs down. You can prepare to grab aggro on them by casting your Death and Decay into the cloud just before they disperse and reveal the mobs. The tentacle puts out a beam that can be interrupted, and since it's relatively low-health and stationary, I prefer to kill it first. Also note that one of the mobs does a nasty knockback, so as the tank, try to face toward the downward slope so it knocks you uphill. You'll fly a shorter distance and take less falling damage.
Benedictus himself comes in two flavors, holy and shadow. In both cases, you will deal with spells that act about the same. There's a basic nuke you can interrupt, so if you can, do so. He will also send out up to three orbs at intervals that will rush at people. When they land, they also leave a patch on the ground, so get out of that or pull Benedictus away from them. The final ability to deal with his a massive wave that will sweep across a large portion of the platform where you fight Benedictus. For the first half of the fight, Thrall will create a Water Shell. This will not only protect you from the wave, but also give you a 100% damage buff, so tanks, try to look for it and pull Benedictus to it as soon as it appears. Unfortunately, for the second half, Thrall will be incapacitated, so you'll need to watch for the wave to appear and get to a safe spot.
Benedictus drops quite a few nice things for death knights. Dual wielders may want to grab a couple Treachery's Bites, while DPSers can get some use out of the Rosary of Light's massive strength, even if the critical strike proc is less useful for us. For tanks, Pauldrons of the Dragonblight offer a nice balance of parry and dodge rating, and Veil of Lies is a decent trinket option.
Learn the ropes of endgame play with WoW Insider's DK 101 guide. Make yourself invaluable to your raid group with Mind Freeze and other interrupts, gear up with pre-heroic DPS gear or pre-heroic tank gear, and plot your path to tier 11/valor point DPS gear.