Oblivion:The Desolate Mine

Quick Walkthrough
# Speak with Burz gro-Khash. He needs you to bring a weapon cache to some guild members at the Desolate Mine.
# Make your way to the mine and take care of any enemies guarding the entrance.
# Once inside, speak with Rienna.
# After discovering how each member prefers to kill goblins, distribute the weapons appropriately.
# Head into the bowels of the mine with the other three guild members and eliminate all standing resistance.
# Once the mine is clear, return to Burz gro-Khash for your reward.

Detailed Walkthrough
This first Cheydinhal Fighters Guild quest - together with the first Anvil Fighters Guild quests, A Rat Problem and The Unfortunate Shopkeeper - is required for advancement in the guild and proceeding to Unfinished Business, but it is completely independent of the other two regarding order of completion. You can receive this quest before, during, or after any of the Anvil quests.

A Simple Weapon Drop
Burz gro-Khash asks you to deliver a weapons shipment to some Fighters Guild members in the Desolate Mine to the northwest. He gives you a bow, a longsword and a warhammer, all three made of steel and completely weightless. The location will be marked on your map. When you get close to the mine, you may be attacked by goblins - a sign of things to come. Inside the mine speak to Rienna, who will reveal that the mine has been infested by goblins. She instructs you to give the weapons to the two other fighters (Elidor and Brag gro-Bharg) standing by the fire. Be sure to give the appropriate weapon to each fighter: Brag gro-Bharg prefers the warhammer, Elidor prefers the sword, and Rienna prefers the bow (which she will take from you automatically).

The Foul Beasts
Once you have distributed the weapons, get ready to combat the goblins. Follow the three fighters into the mine and hack at any goblins you encounter. You will also notice several dead miners. All three fighters subscribe to the discredited school of "rush head first into battle without a strategic plan", which may well end up getting some or all of them killed. Keep up and help them as best you can. They also tend to split up after a point, making it impossible to follow all of them. It is recommended to remain with Rienna, as she is armed with only a bow and more likely to become swarmed than the two other fighters. Elidor is also not well-suited to combat and may require additional supervision. Brag is a hardy Orc and has the most damaging weapon of the three, meaning that he requires less attention. Should you have one of the rare spells that boost the abilities of others, consider using it on your companions, preferably the ones you are not with.

Once all of the goblins are dead, return to Burz gro-Khash for your reward and possible promotion. Your reward is dependent upon how many of the other three fighters survived:
If they all survived, you will get double the usual quest reward (200 to 1200 gold) and one Fame point. In addition to this, people will begin talking about how the Fighters Guild did a good job in the Desolate Mine.
If one or more persons died, you will get only 80% of the standard quest reward (80 to 480 gold). You will not receive any Fame points. You will also have to endure various negative rumors about what happened at the mine.

Any weaponry you take from fallen members' bodies will be removed by Burz gro-Khash (unless you drop the weaponry somewhere before speaking to him). However, any armor will not be taken, so letting some of the fighters die can be a good way of acquiring chainmail or steel armor for low level characters before it would normally appear.

You should also be able to receive a promotion from Burz. If this is the first Fighters Guild quest that you have completed, you will be promoted to the rank of Apprentice. You will then need to see Azzan in Anvil for your next quest, A Rat Problem. If you have already completed both of Azzan's quests, then you will be promoted to the rank of Journeyman. In that case, you next need to go to Chorrol to talk with Vilena Donton and Modryn Oreyn for your next quest, Unfinished Business.

Notes
You can pickpocket the key from Rienna and kill the goblins yourself before speaking to her. If you plan to do this, make sure of two things: 
Do not give any of the fighters a weapon.
Close the door behind you after using the key or the fighters and goblins will run towards each other and meet in the middle, proceeding without any weapons, which practically guarantees that they will all die. (Note that the goblins will run to the beginning and open the door.)
Doing it this way ensures that no one dies, which means that you get the full reward. Save before trying this and make sure that Rienna doesn't catch you, as you will be expelled from the guild if she does. But you can't keep the weapons since they only stop being quest items when they are given to the fighters.

Make sure that you trip the log trap in the back of the mine before the three fighters do, for this can kill them within seconds of exposure.
If all three fighters survive, Burz gro-Khash's disposition to you will increase more than it would if any of the fighters died. This has no great effect on the quest line, though.
The weapons you can take from fallen members' bodies might be handy, since they have a weight of 5, compared to 10, 24, and 39 respectively for a standard Steel Bow, Steel Longsword, and Steel Warhammer.

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