The Furnish Mode lets you equip your inn with all the necessary things. The categories you can choose from the menu are: Common room (for example: tables, chairs), Sleep Room (beds), Facilities (barrels, ovens), Decorative (flowers, paintings), and Outside (chicken coops, outhouses, etc.).
To place an object on the grid you have to choose it from the list. You can turn the objects with the Q and E keys. Holding the Ctrl key allows you to place the objects on the grid with more precision; use the mouse scroll wheel to place the object at a preferred angle. When placing furniture, make sure there's enough space to walk between two objects. Confined patrons will start panicking and destroying furniture.
If no guests are visiting your inn, make sure it's open, and that you have at least one counter, a table, and a chair/bench. When building a room it is important to remember that each object has its traits, telling you of their quality or an effect they will have on your patrons. If you left-click on an object, you can set its priority, see its details, and other options available for the given object. If there's a red, broken gear icon above an object, it means it's not working properly. It may be caused by a lack of a worker who can use it, a lack of a needed resource, wrong room, or in case of a table - no chair connected to it.
Acquiring new objects
The main way of getting new objects is finding and buying them on the map. Progressing the story, upgrading the character, and Adventurer Quests can also unlock new objects.