Complete the main quest “The Forsworn Conspiracy”
Complete the follow-up quest “No One Escapes Cidhna Mine”
Help the people of Markarth by completing at least three side quests for them
Return to Jarl Igmund after helping the citizens
Accept the quest “The House of Horrors” if needed to improve your standing
Speak to the Jarl’s steward to receive the option to buy Vlindrel Hall
Purchase Vlindrel Hall
Speak to the Jarl again to be named Thane of Markarth
Receive the Shield of Markarth and the title of Thane