How do I kill Vincon Traut and the other conspirators?

You can get Backup... as soon as you know Traut's location you can talk to Dethmold. He will give you 4 of his soldiers as backup. So, when you then go to fight Traut, you just have to open the middle door in the room, there the 4 soldiers are waiting to help you in the fight.

Since it is such a small space you can try casting a few Yrden spells (the one that stuns a foe for a certain amount of time). That way you can focus on a single enemy without getting attacked from behind by the others. It's definitely the hardest combat up to that point on the game. It takes some serious maneuvering. The Yrden should definitely help you here.

If you have access to the blacksmith before this fight, make bombs. In particular, 2 or 3 Dancing Stars should be enough to last the fight. Cast Quen before you enter Vincon's dungeon room, since he likes to get a cheap shot off while Geralt draws his sword. Skip through the dialogue, or Quen will wear off before the fight even begins. I would recommend using a short sword at the start of the fight, since maneuverability is very important in these tight spaces.

If you have bombs:

Turn right immediately when the fight starts and toss a bomb straight into the center of the room. A Dancing Star is particularly effective for this since all the conspirators save Vincon have no fire resistance, meaning it's guaranteed to set them on fire shortly after it explodes. Now roll your way to the opposite corner of the room. When the conspirators are on fire or stunned, they dance around and don't attack, meaning they hinder Vincon's progress towards you. This should give enough time for the fire or stun to wear off before he reaches you, meaning it's time to use another bomb. The second Dancing Star should kill off everybody in the room except for Vincon; to accelerate this process, use your sword to attack the weak guards.

If your bombs don't stun or set people on fire, still use a bomb at the beginning, dance your way to the opposite corner and then spam bombs. This should be enough to kill most, if not all, of the conspirators.

If you don't have bombs:

As noted in spugsley's answer, Yrden is a very effective spell to stun one enemy so you can focus on the ones coming from the other side briefly. Take advantage of this to kill one or two conspirators before using another cast. This is best used in one of the room's corners, since that way there are only two ways from which your enemies can approach.

In either approach, making your way over to the opposite corner ASAP is very important because under no circumstances do you want to engage Vincon Traut before all the other conspirators are dead. He has way too much health and inflicts far too much damage, meaning he's the sort of opponent one needs complete focus on to kill.

Once Vincon is by himself, normal combat tactics apply. Either use Quen for a shield or Yrden/Aard to stun him before rushing in for a few attacks and then retreating once he recovers. Heavy, powerful swords are useful for maximizing damage inflicted on each push. If you're lucky, Aard could give you an instant kill, as well. Eventually his health will wear down and you'll win the battle. Inside Vincon's spoils is an important quest item, as well as your key out.