I just got threw this...
1.) Start the quest by talking to the cat.
2.) Craft poisonous cheese (barrel and cheese should do it or a poison potion and cheese)
3.) Place poisoned cheese at any hole and watch them DIE
4.) Rat King will spawn and carry on about murdering his subjects. It really does piss him off

5.) Attack rat king by casting a spell on him or holding CTRL and clicking on him. *WARNING* He will become upset over this.
The rats should run out and die, spawning the Rat King. If you talk to him, he'll ask you to visit the Rat Palace in the tavern basement. There you can spawn him and talk to him.
You fight the rat king by attacking him. For me I had a glitch that made him invulnerable to attack and had to put the game on easy to make him vulnerable. All my damage was doing 0 until changing the game setting.
This is pretty much what stopped me playing until the next patch comes out, games is just too full of bugs for me to deal with.