There is no special interaction with any bosses in order to get the quest done. The boss kills are simple kill tasks that are completed on the boss's death in World of Warcraft.
The Pit of Saron
Here you'll discover a ton of Alliance/Horde slaves are working in the pit. You need to free 15 slaves and Garfrost dead to advance. Kill the enemies near the slaves to release them. You'll get 15 in no time. Then head up to Garfrost for a fun battle.
Just want to hug you with big weapon. Garfrost is a three phase battle where he doesn't like you and it shows. He can throw boulders and comes with a room packed with baddies. Kill all of the baddies in his room and then focus on him. In the first phase he'll throw rocks and beat on the tank. His attacks do apply Permafrost which increases frost damage done by 10%.
When phase 2 starts he'll stomp the group and run off to a forge. Let any debuffs tick off and meet him again. This time he'll do 50/100% more frost damage. Keep dodging boulders and avoid his Chilling Wave which is an AoE cone effect in front of him. In phase three he'll boost his frost damage to 100/200% and cast Deep Freeze which snares a target.
So dodge boulders and smash his face in. When that is done you'll have to move on over to Krick and Ick to open the path to the final boss for the quest you'll be given here.
Krick and Ick are weird, to say the least. Clear the area around Krick and Ick very well because adds will wander into the boss area frequently if you don't. When you aggro him the fight will become a tank and spank with a little bit of a dance. He'll throw poison on the ground which you'll need to move away from and he'll throw bombs on the ground that will get bigger and bigger before they explode. They'll follow your feet.
So just drag him around, avoid bombs and poison, and kill him. Then go through the tunnel. The tunnel will start collapsing so watch where you stand to avoid too much unnecessary damage.
At Scourgelord Tyrannus you'll have to worry about two things. Rimefang will be shooting ice at people and he'll Empower which makes him do double damage. Rimefang will put frost paths on the ground that you can use to kite him around to avoid the damage if your tank can't take the heat. Oh, watch out for The Overlord's Brand too. This ability transfers your damage to the tank which is a bad thing. Just stop doing DPS if you get hit with it.
After that you'll be treated to sort of a mini-cinematic and be sent on off to The Halls of Reflection. This guide should explain things so you don't have to figure things out as a group wants to run as fast as possible through the Pit of Saron instance in Woeld of Warcraft.