The mansion is divided into areas that are unlocked one after another. It takes 3–6 game days to renovate each area, something you do by completing all the tasks in them.
Each task requires 1–5 stars you earn by beating match-3 levels. It takes more time to complete certain tasks, though you can always speed up the process if you don’t want to wait.
Follow your progress and keep track of your current tasks in an in-game tablet you can find in the bottom left corner of the screen.