During the Main quest line, after slaying the first dragon outside of Whiterun, the player is prompted to return to Jarl Balgruuf the Greater. During the return, the player may hear the thunderous call of the Greybeards summoning him/her to High Hrothgar. Jarl Balgruuf will subsequently recognize the player as Dragonborn and grant the title of Thane. As Thane of Whiterun, the Dragonborn will be granted a Housecarl. The title of Thane will also provide the opportunity to buy Breezehome, a house near the entrance to the city, from Proventus Avenicci for 5,000 septims. This purchase will unlock the Citizen achievement/trophy.
Decorating / UpgradingEditAfter purchase, the Breezehome it looks empty and dull and there may be a squatter leaving the home after realizing it has been purchased. The Dragonborn must purchase the various room upgrades from Proventus Avenicci. The cost for the purchase of the decoration is about 1,800. The Housecarl will remain at the house if the Dragonborn does not ask for her help.
There is a bug where, after purchasing Breezehome, the player is not given the option to buy decoration for the house from Proventus Avenicci. Sometimes this can be fixed by exiting and re-entering the game (tested on PC & PS3 only).
After buying the alchemy lab, it still shows up on the list and isn't upgraded in your home, even if you buy it a couple times.
There are many other types of houses to buy in the game; however, Breezehome is typically the first opportunity a player encounters, as well as the cheapest available house. Also, because Whiterun is discovered so early, fast traveling back and forth is relatively easy.