Speak to Sheogorath and chose to become the Duke of Mania. He will instruct you to poison Thadon and take a sample of his blood. Speak to Wide-Eye, who'll point you towards Greenmote, the deadly poison that you need. After finding the Greenmote in the Greenmote Silo, make your way towards the Duke's quarters. Locate his meal and wine and poison them with the Greenmote. Return to the Duke's dinner table at 8pm and take a seat. You will see Thadon die. Take his blood and return to the Sacellum Arden-Sul to complete the ritual. You'll now become the Duke of Mania.
Refer to Ritual of Mania for more information.