The Great Gate
This is a timed quest and, as far as I know, it's the only one in the game. You have about 13 or 14 minutes (real time) to get to the Great Sigil Stone. That means you can't afford to do a lot of exploring or looting, although you've got more than enough time to loot whatever you might kill on the way and grab loot that's in your path. Since you're probably not going to be taking a lot of time to be sneaky, make sure that you take a decent supply of healing potions/spells. If you've been closing other Oblivion Gates up to this point, the time limit is more than sufficient. You've already got a very good idea of what to expect, know what needs to be done and how to do it. If you've only closed the gates near the other cities, the time limit should be enough, but inexperience will be working against you.
When you appear, you're at the south end of the area, looking north at a gate that's in the process of opening. There will probably be a couple of lower-level daedra (Scamps, Clannfear, etc.) just on the other side of the gate and a Dardric Siege Crawler headed for the Great Gate. That's where the time limit comes in. If the siege crawler makes it to the gate, Bruma is toast.
There are towers on either side of the gate and it really doesn't matter which one you choose to enter. I generally prefer to take the left (west) tower, but both towers are pretty much the same. I just find the western path to be a bit easier with my style of play. Climb to the top (you'll run into a Dremora inside) and exit to the north over a bridge to the next tower. This northwestern tower should not have a Dremora inside (which is probably why I go that way). You'll need to go down at the northern tower and then take the northern exit to get out onto another bridge.
This bridge has a break in it, but if you've got a decent Acrobatics skills and Speed, you can clear the jump quite easily. You'll land pretty close to some lower-level daedra and Dremora who will want to be putting a hurt on you, while a turret to your north is going to be lobbing fireballs at you. Take care of business and keep going north to the bridge running across the one you're on. If you've got a great Acrobatics and Speed, you might be able to jump up on the bridge in front of you. The rest of us will have to be more creative. Run under the bridge and make a left-handed U-turn to find a narrow opening that will let you run up onto the bridge in front of the door to the tower. You'll note that the gate to your left is closed and blocking your progress toward the main tower. Not to worry.
Enter the tower and deal with whatever daedra are inside, then climb to the top of the tower and pull the gate lever. There is a Blood Fountain and Magicka Essence inside this tower if you need them. Then go back down and out the door you came in through. You'll see the steps leading to the entrance of the main tower when the gate opens. There will probably be a Dremora or two protecting those steps and let's not forget the turrets that are still firing. If you position yourself well, the gates will block the turret fire, letting you concentrate on the Dremoras. When they are history, enter the main tower.
The main tower is pretty short in comparison to all of the other towers you've had to deal with. There is only one intermediate level between the bottom and top levels. If time is critical, hang a left after the three dropping swords rather than searching everything. There are two Sigil Keepers in the tower, one on the ground floor and one on the top floor. You'll need to grab the Sigil Key from one of them to get into the Sigilum Sanguis at the top. The Sigilum Sanguis for this tower only has two Dremora instead of the standard three, but it also only has one loot container, and that's off to one side rather than on the platform with the Sigil Stone.
Once you grab the Great Sigil Stone and the destruction animation finishes, you'll reappear back in Bruma. The siege crawler will drop a normal Sigil Stone for you since you're going to have to give the Great Sigil Stone to Martin. All of the soldiers are cheering, but you should check bodies to make sure that Jauffre and Baurus made it. There should also be a few dead Dremora to help you make up for the loot you weren't able to get during your little jaunt into Oblivion.
Congratulations! You've made it through the most maddeningly frustrating fight of the entire game. Enjoy the cheers, give the Great Sigil Stone to Martin, pick up your regular Sigil Stone from under the crawler and get ready to go to Paradise.