You'll need to send a tank to each side and split power leveling your DPS and healers into roughly equal parties. The DPS split is particularly important because Stalagg and Feugen have to die within 5 seconds of each other. An interesting twist is that they'll periodically do an ability called Magnetic Pull which yanks each other's tank across the room (i.e. if Tank A is tanking Stalagg and Tank B is tanking Feugen, Magnetic Pull will leave Tank A tanking Feugen and Tank B tanking Stalagg). Each tank inherits the previous tank's threat on them, so it has no real bearing on how you do the fight, but it's fun to watch. Tank damage isn't particularly bad. Stalagg does more melee damage than Feugen, but Feugen augments his with some magic.

Your raid leader will need to /focus whichever mob he/she's not on in order to call out whether DPS needs to be increased or decreased on a particular side. Ideally you want Stalagg and Feugen power leveling down as quickly as possible because Feugen has a mana drain that could leave your casters and healers in bad shape, but ultimately it's more important that the mobs die together than that they die quickly.

After they're dead, there's an interval of about 15 seconds before Thaddius himself actually becomes active, so the next step is defeating The Ledge Boss. If you have problems with the power leveling jump (some people do, especially if they're lagging), a run speed enchant on your boots, or a run speed potion or ability is usually enough to ensure you'll jump correctly. After the Construct Quarter's been cleared, you can always come back and practice!