To buy the Solitude house, you must first complete the "The Man Who Cried Wolf" quest for Falk Firebeard by clearing out Wolfskull cave (which is not a hard task for those who would consider themselves good), and then you must talk to Jarl Elisif the Fair, and she will send you on a short quest to place a war horn on the Shrine of Talos. That is not hard either, but as a warning, there is a dragon guarding the shrine. When you complete that, return to Solitude, then talk to the Jarl, and you will be able to buy the three-story house for 25,000 gold. It cost more for upgrades, and I recommend buying the Arcane Enchanter so you can do the armor duplication cheat.
Added by: MNvikingsfan1 May 13th 2012, ID#8397