Allies for Bruma

This quest and the "Defense of Bruma" quest activate at the same time. You get this quest from Jauffre and you get the "Defense of Bruma" quest from Martin. The biggie is Martin's quest, but this one is going to determine how much extra help you'll have available for Martin's. You're to go visit the other cities and get them to send help/reinforcements to Bruma before the daedra attack the city.

There are a couple or three ways that this can play out. Oblivion Gates have opened near the other six major cities in Cyrodiil (Anvil, Bravil, Cheydinhal, Chorrol, Leyawiin and Skingrad). It's entirely possible that you have already closed all of them. In that case, all you'll need to do is travel around, collect your thanks and promises of support and then report back to Jauffre and activate Martin for the biggie.

It's also entirely possible that you haven't closed any of them (except Kvatch, but there's still more to do before you'll get help). Unless you've been adventuring on your own, the Main Quest hasn't sent you to any of these cities except Kvatch. In that instance, you'll need to go around to each of the towns, close the Oblivion Gates at each one, then go talk to the appropriate person to get the support that Bruma needs.

The third option is in the middle - you've closed some of the Oblivion Gates, but not all of them. In that case you'll need to go finish up the job. Sort of. The point is that this quest is entirely optional. You can do some, all or none of it. You're already guaranteed help from Captain Burd and his soldiers. You should also have help from Jauffre (and Baurus, if he's still alive). And Martin will strap on a sword and pitch in, too.

That leaves you as the decisive factor. If you're big and bad enough to run interference between the existing forces and three daedric invasion forces (remember from Jearl's note that there will be three minor gates opening before the Big One can open), then you can go for it. If you're not that big and bad, then you should bring in as many reinforcements as you can.

An Oblivion Gate may have opened outside of the Imperial City. It's a random thing, but there are a couple of places next to the Imperial City where a gate can open. However, closing them won't net you anything except the standard Fame boost for closing a gate near a city. Chancellor Ocato flat out refuses to send any support to Bruma, but you're welcome to ask him. There is one other 2-point gate that opened near Fort Sutch (north of Lord Drad's Estate, which is just north of where the highwayman jumps you on the road between Anvil and Kvatch). It's defended by a few Imperial Legionaires, but helping them by closing the gate will not get you any help for Bruma. The extra Fame point is nice, though.

Except for Cheydinhal and Kvatch, which have their own little side quests, the process is the same: close the gate, speak to the appropriate count/countess to get a promise of support, move on to the next one.

For Kvatch, you had to close the Oblivion Gate in order to collect Martin in the first place. However, if you haven't helped Savlian Matius clear Castle Kvatch of the remaining daedra (Battle for Castle Kvatch), you'll need to do that before he'll send any help.

For Cheydinhal, you'll need to rescue the Count's son, who charged into the gate with his Knights of the Thorn a couple of days earlier. The kid and his remaining companion are both still alive when you get to them and it's your job to keep them that way until you can close the gate. I find this particular quest to be the most annoying, but that's due more to my playing style and the complete lack of intelligence on the part of the Radiant AI than any great difficulty in closing the gate.

So what kind of help can you expect out of all of this? It kind of depends. Bravil will send a high-level guard captain. Cheydinhal will send a high-level guard captain and a soldier if you manage to return the Count's son in one piece; you'll just get the soldier if the kid dies. Anvil and Chorrol will send a couple of regular soldiers each. Leyawiin, Skingrad and Kvatch will cough up a single soldier apiece. If you gather everyone who can possibly be gathered, plan on about 14 or 15 people, including Jauffre, Baurus, Martin and Captain Hurd. About half of them being decent fighters and the rest will be regular soldiers.

Once you have gathered all of the troops that you're going to gather, talk to Martin to kick off the Defense of Bruma quest. Note that until you go to the chapel and tell Martin and the Countess that you're ready, you can close more of these gates and add more soldiers to what you've already assembled. It's the invasion that actually ends this quest.

Anvil
the gate is a bit northwest of the main city gate and sitting right on top of a wayshrine. There is nothing really different about the tower on the other side except you'll have to traverse a couple or three Oblivion Caves to get there. Talk to Countess Millona Umbranox to collect your troops.
Bravil
the gate is northeast of the main gate, occupying the ruins of a fort on a nearby hilltop. The most difficult part of the towers on the other side is getting into the main tower. Heading east from the portal is probably the easier way, but it can also be done by going west. If you head east, traverse a couple of Oblivion Caves in order to get into a side tower, then climb to the top and pull a lever to open a gate that will allow you to enter the main tower. If you head west, find and traverse an Oblivion Cave to get under some lava. Then exit and continue overland until you can get into a side tower where you'll need to pull a lever on the top level to open a gate that lets you get to the main tower. Once you're in the main tower, it's pretty much a straight shot from there. Talk to Count Terentius to get the guard captain dispatched to Bruma.
Cheydinhal
you'll need to work your way around and through some Oblivion Caves in order to get to the Count's son (Farwil Indarys) and his companion. If your Acrobatics skill is decent enough, you might be able to just climb down the mountainside and bypass the caves. Once you've hooked up with them, you'll need to charge across the bridge in front of their position. The gates will open automatically, so you don't have to worry about that. Once you've cleared the bridge, you can enter the main tower. Once you're in the main tower, it's pretty much the same as any other Oblivion Sigil Tower. The hard part is keeping Farwil alive in spite of his love for frontal attacks and outright stupidity. I have seen this guy jump into pools of lava to fight a critter that wasn't dead yet, but would have been if he had just waited a couple of seconds. When you've retrieved the Sigil Stone and closed the gate, talk to Farwil. You'll be made an honorary Knight of the Thorn with your very own medallion (slight boost to Speechcraft) to prove it. Dad, however, will be a bit more generous. You can choose between two weapons: Thornblade (has a Disintegrate Armor effect) or the Staff of Indarys (Damage Strength and Shock Damage effects). Trinkets and baubles are nice, but don't forget to ask for your troops.
Chorrol
the gate is on a small hill just south of the city gates (very easy to spot). You'll see the central tower surrounded by several side towers and some massive gates (all closed). It looks complicated, but it's really just a matter of working your way around either east or west until you can get into one of the four side towers that are accessible from the outside. Climb to the top and open a gate. Go back down and enter either the Earthquake tower (east) or Hurricane tower (west), climb to the top of one of those and use the bridge to get into the main tower. It's a standard Sigil Tower from there. Talk to the Countess after you've closed the gate to collect your troops.
Leyawiin
you start off with one Oblivion Gate on a small island just outside the city. However, when you close that one, a second one opens up almost immediately just to the southeast of the first. This second gate is the one that has to be closed in order to get the soldier. I just plan on closing two gates and call it even. When you enter the second gate, you'll see a bridge with a dead horse and a daedra of some kind patrolling. The main tower will be directly in front of you, but the bridge is broken. It can be jumped with super Acrobatics skill and Speed attribute, but it's much simpler for us mere mortals to use the Oblivion Cave off to the left. You'll come out in a tower with a broken Corpse Masher. Go up one level to get to a bridge that will take you to another tower where you'll need to open a gate that will allow you entrance to the main tower. Standard tower after that. Talk to Count Caro to collect your soldier.
Skingrad
this one also has two gates. One of them opens on top of the wayshrine that near the entrance to the castle; the other opens up in the small graveyard just outside of town. I believe the wayshrine gate is the one that gets you the soldier, but I just play it like Leyawiin - I plan on closing two gates. When you enter Oblivion you'll be below the center of a bridge with two towers between them: one to the left and one to the right with both entrances accessible to you. No daedra in sight. You can enter either tower, but I prefer taking the one on the right first, more from habit than anything else. Work your way to the top of the tower and pull the lever. This unlocks the first of two locks. Then use the door at the top of the tower to cross a bridge to the top of the other tower where you'll release the second lock and extend the bridges between the two side towers and the main tower. Then fight your way down the second tower (you can't go back to the first) until you can cross the bridge to the main tower and then head up to snag the Sigil Stone. After you've closed the gate, head for the castle. Unlike the other counties, Count Hassildor doesn't keep regular office hours. Instead you'll need to talk to the steward. This will be either Mercator Hosidus (if you have not completed the "Ulterior Motives" quest for the Mages Guild) or Hal-Liurz (if you have). They will fetch the Count if you use the "allies for Bruma" thread. Unless you're in the Mages Guild or manage to contract vampirism, this will be your only contact with Count Hassildor, but he'll send along a soldier as thanks for closing the gate.