The Citadel of Flame (CoF) dungeon currently offers one of the most lucrative ways to earn gold: farming path 1 (scout Ferrah). The run can be finished in 7-15 minutes depending on your group, and usually yields 80s to a 1.2g. However, it has a few mechanics that you need to know to have a successful run.
Below will be a step by step description of what to do from the moment you're starting path 1.
From here on, I'll try to keep everything as concise as possible.
Breaking through the wall
At the very start, an NPC will blow up a wall for you. Behind it are a handful of mobs and two flame turrets.
Kill the turrets first, then kill the mobs.
After the fight you can see a green mob named 'Slave Driver'. He will turn red and be the first boss. There will also be a Flame Legion Effigy. Ignore the Effigy and kill the slave driver instead, when it's dead the Effigy will die too. (Optionally, you can get some drops from the effigy if you damage it a little during combat.)
After killing the slave driver, you'll be crossing a bridge. Ignore all the mobs on it - run past them, into the back of next room.
In this room, there will be several waves of Flame Acolytes and an infinitely respawning pool of trash mobs. Kill the Flame Acolytes - easily recognized by crossed swords above their heads. When you've defeated a wave of Acolytes, break aggro until new ones have respawned. Once all Flame Acolytes are dead, the rest of the mobs will disappear.
There are two places where you can easily break aggro.
The first location is down the corridor that's (when you first enter the room) on your left. After running through the corridor, there's a big rock on the left in front of the lava wall. Jump on it and you're safe. The downside to this place is that you can't easily see the Acolytes to know if they respawned: You'll have to keep an eye on your minimap for sword icons to appear.|
Here's a YouTube video.
The second one is much closer to the Flame Acolytes. When you first enter the room, there's a rock on the right you can walk up on. Then, jump forward (using swiftness or dodging and jumping simultaneously helps) to the ledge. This jump requires some practice, but you have a good view on the Acolytes when they respawn. Make sure you jump to the lowest part on the left to make the jump easier.|
Here's a YouTube video.
You'll be going through a corridor with two braziers at the start, fireballs rolling sideways in the middle and and three braziers in the back. The fireballs are one-hit-kill. Take off your armor to avoid it from being damaged.
Take a flame from one of the first braziers, and place it in one of those at the end. When all three are lit the fireballs disappear and the next room opens. To get across, walk at the very side of the corridor. Don't run all the way at once, hold still until the ball in front of you rolls away from you.
Here's a YouTube video.
If you die, the balls rolling over your corpse make it impossible to get resurrected before your partymembers have completed this stage. Instead of waiting, use the waypoint in the Flame Acolyte chamber to give it another try.
If there's a Mesmer in your group, have him put up a portal. (If you're a Mesmer, place your portal, run up a bit and use blink. That should get you past all other fireballs.)
Flames go out if you hold them too long or if they're in the braziers for too long.
Always try to run this with three people simultaneously. If one of you gets hit, make sure the others do not place their flames yet until someone else (almost) made it across.
In the next room, one of the players will have his unique role.
4 players: There are four little stumps coming out of the floor on your right. When you get close, a bubble appears around it. Every player should be in a different bubble. If you're not in your bubble, the door to the next room can't be opened. Survive, and stay in your bubble, until the door is opened.
1 player: this role is usually fulfilled by a DPS build - Eles or Warriors in particular. While everyone else is standing in their bubbles, the gate will open allowing you to access a yellow pedestal. It's indicated on your map with a red icon. Attack it with everything you've got. When it's broken, proceed into the next chamber. Also, make sure your party knows the door is open.
Next to the pedestal will be a Godforged Hellspawn. It has a very strong flamethrower attack, that can be deadly for nearly any build. When you run through the gate, before attacking the pedestal take the path to the right. You'll pull the Hellspawn as you go. Jump out to the right again, and go back to the pedestal. Once you break aggro the Hellspawn won't come back to the pedestal, allowing you to destroy it more easily.
These are the bubbles the four players have to be inside of. They appear when you get close enough to the stumps. Make sure there's one player in each, otherwise the gate can't be opened.
The boss is fairly straightforward. It summons crystal shards, which give him regeneration stacks. If your group has a Mesmer, have him cast feedback before the shards are summoned for heavy damage. Try to stay close to him, as you'll evade many of his attacks. Summoned crystals knock down, so use stability or dodge when you see the red circles appear. Other than that, just keep attacking him.
If his regeneration is higher than your group's DPS, destroy some crystals. When possible, aim your AoEs to hit both the boss and a nearby crystal.
If you are downed, you can rally by destroying a crystal.