To reach the rank of Madman, you must complete the quest “Understanding Madness”, which has two sub-quests: “Lady of Paranoia” and “Addiction”.
Understanding Madness – Speak to Sheogorath about your previous quest in Xedilian and he will reward you with the power to summon Haskill for advice and information. He insists that you use the power before he will talk to you again. Humor him and summon Haskill once. Sheogorath will then instruct you to speak to both Thadon, Duke of Mania, and Syl, Duchess of Dementia, so you can join their courts.
Lady of Paranoia – Talk to Syl in the House of Dementia and she will appoint you as her Inquisitor with the job of unearthing a suspected plot against her. Use her torturer Herdir to question the steward Kithian. He will point you towards Anya Herrick who reveals that Ma’zaddha is involved in a plot, but Ma’zaddha refuses to speak, claiming that you have no proof. Travel around Crucible and talk to the citizens until someone tells you that Ma’zaddha has been meeting with Nelrene. Around midnight, hide near Ma’zaddha’s house and listen to the conversation between the two conspirators. Once Nelrene leaves, talk to Ma’zaddha again and he’ll confess to a plot, asking you to meet him the next day for more information. When you return to his house the next day, you’ll find him dead. Take the key off his body and go to his room where you will find evidence in the form of a note a ceremonial sword. Take both items and question Nelrene who will confess that Muurine is the leader of the plot. Interrogate Muurine until you get a confession, report to Syl, and then witness the execution in the Torture Chamber to finish the quest.
Addiction – Talk to Thadon in the House of Mania and he will request that you obtain the Chalice of Reversal for him. Talk to his steward Wide-Eye and she will direct you to Dunroot Burrow. Travel to the burrow and kill the Elytra at the entrance. You have to loot the Felldew off of its body and ingest it to pass the Barrier Membranes that serve as doors in the burrow. After a short period of time, you’ll go into withdrawal and have to kill more Elytra to get the Felldew necessary to reverse the withdrawal symptoms. Work your way through the burrow until you get to the final area where you’ll find three hostile characters and the Chalice. Kill the NPCs and take the Chalice, which will immediately reverse the effects of the Felldew addiction. Exit the burrow and return to Thadon to finish the quest.