Start by talking to Rat Burgiss at the crossroads between Al Kharid, Varrock, and Lumbridge. Choose 'Hello there!' and he will explain his name is Rat Burgiss. He will explain how his cart was attacked by outlaws, and that they stole some important papers from him. Offer to get them back for him.
Go to the outlaw camp and kill the outlaws. They will drop Rat's papers. Collect all five, and use them on the folder that Rat gave to you. When it's full, return to Rat. He will then ask you to take a letter to someone named Surok Magis in the Varrock Library.
Head to the Library, located on the ground floor of Varrock castle. After insulting you, he will take the letter and burn it with magic. He will then let you in on a secret: he's on the verge of learning alchemy. But, he needs a gold bar and a wand infused with chaos magic.
He will give you a metal wand. He will tell you to take 15 chaos runes and the wand to the chaos altar. Using the wand on the altar will create the chaos wand. He will give you a diary, and tell you there is another book that may help you find a shortcut to the Chaos altar.
Option 1: Dagon'Hai Caves
Head north-east of Varrock to the Saradomin Statute. You will see Anna Jones sitting on a bench there. Talk to her, and she will give you a bronze pickaxe. Use the pickaxe on the statute you open a whole into a tunnel.
Walk through to the end of the tunnel, and enter through the portal. Finish going through the Chaos Altar maze.
Options 2 & 3: Wilderness
The other options are to go through the Wilderness. You can choose to go to the Chaos Altar, though this is not recommended, due to Option 1 bringing you further into the maze.
The last option is to go to through the Abyss, but is only available if you have completed the Abyssal mini-quest. This option is highly recommended, due to it taking you directly to the altar, by-passing the maze. Make your way to the inner layer of the abyss, and into the chaos rift on the north side.
Use the wand on the altar to infuse it. Return to Surok in Varrock. Give him the items, and he will then give you a letter to give to Rat. Return to Rat, and give him the letter.
He will explain that he is actually the Commander of the Varrock Palace Secret Guard. He will explain that Surok intends to use a mind controlling spell on King Roald, and that a contact of his, Zaff, has been working on a spell to counteract it.
Go meet Zaff, located in the staff shop near the center of Varrock. Tell him Rat Burgiss sent you. He will explain that the king needs to be near-death for the spell to work. He will give you a beacon ring to summon him when the time is right.
You will be made an honorary VPSG to be able to arrest Surok. Read the instructions for the Beacon Ring, then head into the library and confront Surok. He will refuse arrest, and his will cast his mind-control spell on the king. Attack him until a message appears in your chatbox saying that now would be a good time to summon Zaff. Right click the ring and summon him.
The king's mind will be restored, and he will be teleported to safety. Surok will then attempt to teleport, but Zaff will block it. Return to Rag Burgiss to claim your reward.