You might have noticed that Oblivion Gates have opened outside of all of the major towns in Cyrodiil. Perhaps you've even closed a few of them (it's OK if you haven't - you'll need to do it anyway in the "Allies for Bruma" quest coming up next). Bruma is no exception, except that Captain Burd and his guardsmen want you to show them how to close one of these gates. So you're about to be a teacher (translate that as "babysitter").
I don't mean to be so derisive of the good Captain and his men, but they think the best tactic is the frontal assault. In contrast, I firmly believe that you don't have to fight something if you can kill it before it knows you're there. Patience, stealth and a good backstab; that's the ticket. Burd and his men will behave like normal NPCs - if they see something, they attack it. All of which puts a major kabosh on my playing style, so I either have to range way ahead of the pack to take out anything before it can take them out (hard to do since they'll run like crazy to keep up with me) or I have to stay with the pack and play field medic to make sure that no one dies (or at least no one important). It took me a while to figure it out, but there's a third option (sort of) - don't take them.
What I mean by that is that if you want to stick with your playing style, you should not talk to Captain Burd or any of his men, but just run right into the Oblivion Gate. The other side is just like any other Oblivion Gate except that getting to the central tower involves working your way around a daedra-infested circle. The daedra you encounter will be pretty much the same as behind any other Oblivion Gate (leveled Daedra) and inside the tower is only one pre-placed Dremora, the Sigil Keeper, and the rest are pretty standard. The Sigil Keeper has the key that will let you into the Sigilum Sanguis where the only difference is that there are four leveled daedra instead of the normal three.
The catch comes when you try to take the Sigil Stone. If Captain Burd is not with you, you won't be able to take it. Instead you'll get a message telling you that you need to bring Captain Burd to see how to close the gate. Ooops.
All is not lost, however. If you'll run back down into the Corridors of Dark Salvation, you should meet up with Captain Burd and a couple of his guards. You can now take them to the Sigilum Sanguis with nothing in the way to attack them. Lead them back up to the Sigil Stone, take it and close the gate. When the detonation animation finishes and you are back outside of Bruma, you can talk to Captain Burd (who says that he and his men can handle any future gates that might open) and complete the quest.