Flame Leviathan is the first boss in Ulduar, and rather unique as it is the only fight in WoW at the moment where you completely abandon your class for the whole fight. Gear does matter in this fight, though, as each vehicle will have more health based on a sum of the item levels in your gear, minus your tabard, shirt, off-hand and ranged/relic.
So, before you hop in a vehicle, put on all your highest ilvl gear. This only applies the the driver of the vehicle (all the vehicles in 10-man have 2 slots, one for a driver and one for a passenger.) After entering the vehicle, you can safely remove all of your gear to save yourself a repair on a wipe. This is helpful for learning the fight.
This guide and all following guides are structured such that you should only have to read what your role specifically is doing in the encounter to perform it correctly. Each section has a general description, followed by a subsection for each role. If you are learning a fight for the first time with your guild, I would suggest only reading the parts that apply to you.
The first thing you want to do is talk to Brann Bronzebeard to start the encounter in easy mode. In this mode, you will not have to worry about destroying towers, you can just head straight for Flame Leviathan. Do not talk to the Lore Keeper of Norgannon to begin this encounter unless you want to do the battle with at least one tower up (though the strategy presented here is perfectly applicable to 1 tower up.) If you accidentally talk to the Lore Keeper to start the encounter, but want to down Flame Leviathan with no towers up, you can safely run out and reset the instance, rather than going and destroying all the towers.
After you talk to Brann, the vehicles will become available. There are three types of vehicles, and there are two of each: the siege engine, the demolisher, and the salvaged chopper.
Here's a look at the roles in the encounter:
Siege Engine: The siege engine is responsible for interrupting Flame Leviathan's Flame Vents ability.
Siege Engine Gunner: This guy is responsible for shielding the siege engine, shooting down pyrite, and lighting oils on fire.
Demolisher: The workhorse of the group. This guy is responsible for stacking pyrite on Flame Leviathan for high damage.
Demolisher Gunner: Shoots down pyrite, picks up pyrite, ignites oils. This guy needs to be always aware of the Demolisher's pyrite supply so that it can do the most amount of damage possible.
Salvaged Chopper: Responsible for moving pyrite to more convenient locations, and picking up anybody whose vehicle was destroyed.
Note: I have purposely excluded the ability "Throw Passenger" and related abilities. They are not used in this strategy and highly unneeded on easy mode Flame Leviathan. It's a little more complicated, so don't worry about it for now until you start working on Flame Leviathan with 2 or more towers.
The trash on Flame Leviathan is a great place to learn the ins and outs of your vehicle. There are many dwarfs for steamrolling over, plus some larger mobs, and some pillars from which more dwarves will spawn.
Steam Engine: Your job for the most part is to take damage. You are, quite literally, the tanks during the trash. If you are surrounded by dwarves, use your Ram ability. The Steam Rush ability is largely unnecessary on trash, but part of the fun of driving a siege engine, so go crazy! When you get to Flame Leviathan's area (pictured above,) move to the back right side of the arena and wait for the rest of the raid to get ready.
Steam Engine Gunner: Shoot down pyrite, and attack large trash mobs and helicopters. If your Steam Engine starts taking a lot of damage, activate your Shield Generator.
Demolisher: Use Hurl Boulder to AoE down the packs of dwarves. Use pyrite on the mechanical spiders, the giants, and the pillars that summon dwarves to down them quickly. When you get to Flame Leviathan's area (pictured above,) move to the back right side of the arena and wait for the rest of the raid to get ready.
Demolisher Gunner: Shoot down pyrite, and pick up pyrite if you notice any deficiency in your Demolisher's supply. You can do a fair amount of DPS, so be sure to use Mortar to help shoot down large mobs and pillars.
Salvaged Chopper: Your main source of action will be if someone else screws up to get their vehicle destroyed. In that case, you need to pick them up, drive them to the entrance and drop them off so they can get a replacement. You will also round up dwarves if your raid is doing "Dwarfageddon." Finally, positioning pyrite so it's easier for the Demoisher Gunners to grab is probably the most helpful thing you can do here. When you get to Flame Leviathan's area (pictured above,) move to the back right side of the arena and wait for the rest of the raid to get ready.
When you get to Flame Leviathan's arena, everyone should use a replenishment pad if they need it (there's an achievement if no one uses it.) Then have everyone group up into the right corner opposite where Flame Levianthan enters (pictured here.) When you finish off the trash here, Flame Leviathan will come barreling out, so be prepared and stay in that corner! Before pulling the final trash, have your gunners shoot down a healthy stock of pyrite. When everyone is ready, and there's plenty of blue stuff on the ground (don't forget you can use the Salvaged Chopper to bring some pyrite to a more convenient spot,) kill the trash.
Flame Leviathan will target a Seige Engine or a Demolisher for a short time or until they die. Everyone's main priority is to run away from Flame Leviathan if he is chasing you (this is announced in a raid warning.) Ideally, when Flame Leviathan is chasing you, you will be able to kite him through a flaming oil patch, which will slow him down and deal damage to him (it won't deal damage to you, so you can drive through it yourself.) Here are the other things you should do, according to your role:
Demolisher: Your job is to make sure that your stack of Pyrite is always at 10. When the battle starts, if you aren't the first person being chased, stack your Pyrite to 10. Once your Pyrite is at 10, start using Hurl Boulder so you aren't running out of pyrite so quickly. The Pyrite debuff lasts about 10 seconds, so if you use a rotation of "Pyrite, Hurl Boulder, Hurl Boulder, repeat," you should always have the Pyrite 10 stack debuff up, while not taxing your gunner too much into having to pick up pyrite from the ground. Your range is pretty high, so you should always be near pyrite for your gunner to pick up. If you are chased, don't worry about stacking pyrite, just make sure you don't die!
Demolisher gunner: Shoot down pyrite as needed during the battle. Keep your driver in heavy supply of pyrite and let him know when you aren't near any you can pick up. You can also fire shots at Flame Leviathan and the oil spills to ignite them. If Flame Leviathan is chasing your driver, save the speed boost for when Flame Leviathan is almost in striking distance (but before he can hit you.)
Siege Engine: If you have DBM, your job will be a little easier. You are to follow Flame Leviathan at a close enough distance to interrupt his Flame Vents ability with your Electroshock ability. DBM will warn you 5 seconds before Flame Leviathan changes targets. As soon as you see that warning pop up, turn around and drive away from Flame Leviathan. If he decides to chase you, you're already running away from him. If not, just get behind him again and resume interrupting Flame Vents. Since you cannot turn during Steam Rush, use it only when you have a little bit of room in front of you, regardless of whether Flame Leviathan is about to hit you or not. Do not use it, or any other attack on Flame Leviathan; your Demolishers can easily down him within a couple of minutes on their own.
Siege Engine Gunner: Shoot down pyrite as needed during the battle. Fire shots at Flame Leviathan and at the oil spills to ignite them. If Flame Leviathan is chasing your driver, save the Shield Generator for when Flame Leviathan is almost in striking distance (but before he can hit you.)
Salvaged Chopper: Drop oil spills in front of or near where Flame Leviathan is being kited. Pick up containers of Pyrite and drop them off near the Demolishers.
Flame Leviathan should go down in a couple minutes if both Demolishers are keeping their pyrite stacks up. Congratulations! You made your first step into Ulduar!