After you defeat your first dragon in the main mission, “Dragon Rising,” you’ll be able to head back to Proventus Avenicc, the Jarl’s steward, who’s in Dragonsreach in Whiterun and buy a house for 5,000 gold. All you need to do is buy the house. Nothing more, nothing less. It doesn’t have to be this house though, in fact, there should be one in each major city, but this is the easiest and I’m guessing, the cheapest. Of course, decorating it after with the same chap nets you some cool bonuses, but has nothing to do with the trophy. Decorate that son of a bitch though, yo!