The Pit of Saron
As soon as you enter the Pit of Saron, you'll be greeted by a handful of enemies, including a massive frostwyrm being ridden by Scourgelord Tyrannus. If you engage these mobs, Sylvanas will swoop in to help rescue you. There's some dialogue which I won't spoil, but this is where you pick up the next step in the quest chain: The Path to the Citadel.
All the bosses for the Pit are on the outside of the big, massive circular area. If you stick to the outside wall, you can avoid most of the mobs in the area. The trash is all fairly straightforward and not very difficult, so just blow through them at an easy, steady cadence. The slaves you need to rescue are along the wall, and can be released by simply clicking on their chains.
The first boss you encounter will be Forgemaster Garfrost.
Forgemaster Garfrost is a very large giant. As you go up the ramp to engage him, there will be a dozen or two trash mobs who also engage. DPS should burn these down fairly quickly. They're not very tough, but they would be an unwelcome distraction through the remainder of the encounter.
Forgemaster does a steady stream of damage to everyone in the encounter via his Permafrost. It's a rather annoying effect which is going to make this a bit of a DPS race. Your healers can keep you up through it, but there's no reason to take your time during the encounter.
Garfrost throws large boulders of Saronite on the ground during the encounter. When Garfrost rushes to his forge, have your party duck behind the Saronite to avoid LOS damage.
Otherwise, Garfrost is pretty easy. He forges himself a Frostborn Mace at 66% and 33% life, so those will be golden opportunities to hide behind saronite boulders.
That aside, burn him down, burn him fast.
Ick and Krick
After you've killed Garfrost, you'll need to go fight Ick and Krick. This is really just a gnome riding an undead funky thing. Focus on the undead part -- that's Ick -- and burn him down. He has two actions to which you need to pay attention. First, he'll occasionally give Pursuit to a random party member -- run away from him. Second, he'll throw a Poison Nova from which you simply need to run away.
The Path of Tyrannus
After finding out some key information from Ick and Krick, you'll need to go up a long hallway up to the final boss. The gauntlet to Tyrannus involves some tricky maneuvering. First, you'll have some slightly-more-difficult packs of trash on which you'll need to practice your kill-the-caster-first skills.
As you enter the cave, however, the ice falls down and tries to kill you. There's very clear warning, though, since rune circles appear on the ground. Those circles are warning that rocks and ice are about to fall. Don't stand in it, or you'll take damage.
Scourgelord Tyrannus is probably the most involved fight in the Pit of Saron, which is befitting the final boss. Nonetheless, the game interface itself is pretty friendly about the fight, and gives you lots of warning about the important stuff.
The most important tip I've learned about Tyrannus involves him placing Overlord's Brand on a party member. If the person who has the Brand attacks the boss, it'll do damage to the tank. If the person who has the Brand gets heals, it will heal Tyrannus. Also, keep an eye out for Tyrannus's dark enrage, called Unholy Power. He'll get bigger to give you warning. He hits much harder, but walks slower -- kite away from him and keep a distance until it wears off.
Rimefang the frostwyrm will occasionally fire Icy Blast and Hoarfrost down on the party. Don't stand next to the person who is targeted, and the healer should be ready to take care of that person. Otherwise, it doesn't seem to be a big deal.
After killing Tyrannus, you step into the Halls of Reflection.