I spent more time trying to figure out what to do and how to get space in my inventory than actually picking up items.
From where you get the quest, run out into the main hall and follow the gems to the first room on the right, then continue through the room and there will be more rooms to follow (you're heading towards Mother Shahraz's spot in the normal instance). On the dais at the end will be a chest you turn the quest in to.
Be sure to have tons of empty bag space. I had 9 items types and there were several more I couldn't pick up. Also, when I completed the quest, I got stuck in a loop with my character repeatedly saying "I can't carry any more". By removing one more item, I was able to get all the items it was trying to put in my bags and sell them.
Also, after running out to sell the quest items, the door back inside closed shut, so I couldn't get back in to loot all the windwool and cooking mats that dropped along the way.
The Centurions (Fel Guards) have a silence effect that lasts about 5 seconds, and the Nightlords (Doom Guards) have a fear effect that lasts about 3 seconds, so be careful when pulling large groups.