We are still working on different ways to interact with objects, such as sitting in chairs and opening wardrobes, but for now "left mouse click" is the intended way to interact with the objects in the world.
For example, you can left click on the carriage (try to aim your mouse around the wheels) to bring up the UI to "Drive" the carriage or "Send Home" to send it back to the coach house. Left click brings up the window with your interaction options. Left click "Drive" to begin driving the carriage.
Another example is using left click to "Open" your wardrobe while in the Dressing Room. Left click on the wardrobe object to bring up the UI window. (Since you will, eventually, be able to customize your Dressing Room the option to "Move" the wardrobe is also available.)