To buy a house in "The Elder Scrolls V: Skyrim," the player character has to be in the good graces of a Jarl, or ruler of a territory, and must be named as his right hand, or Thane. You do this by performing a series of tasks for him, such as helping townsfolk, killing dragons, or proceeding in the Civil War questline on the Stormcloak side.
The first hold that the player is likely to become Thane of is Whiterun in the center of Skyrim. After defeating the dragon plaguing the area, Jarl Balgruuf the Greater automatically names the player Thane and grants the right to purchase the house Breezehome near the entrance to Whiterun. To purchase the house, talk to the Jarl's steward, and select the option "I'd like to buy a house." The house in Whiterun costs 5,000 septims, not including the optional upgrades such as an alchemy center, upstairs furnishings and more. In Solitude, Proudspire Manor costs 25,000 septims. Other territories with property for sale include Markarth, Windhelm, Solitude and Riften, each with their own benefits, such as enchanting tables or close proximity to a forge.
With the addition of the downloadable content "Hearthfire," players can build houses in the other territories of Falkreath, Dawnstar and Morthal.