This video shows how to become the Thane of Solitude by completing the quest "The Man Who Cried Wolf" and the misc. objective of placing Torygg's Horn at the Shrine of Talos. After completing both of those quests, you are able to purchase a home in Solitude for 25,000 gold.
You must purchase Proudspire Manor and complete 5 misc. objectives to become the Thane of Haarfingar. The reward for this is the Blade of Haafingar and a lusty Solitude housecarl, Jordis the Sword-Maiden. She is a follower companion and also can be married.
See the next video for purchasing and upgrading Proudspire Manor:
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