Magic’s political aspect

More and more minute elements of the world began to be hammered out as the series progressed over the span of the novels (or movies, if you prefer). Even seemingly mundane aspects of the wizarding world’s political structure began to be disclosed to us.
A few different Ministers of Magic appear, and they begin to play an important role. However, we never really discover how the wizarding world’s political system works. Are elections held? Who chooses the leaders? Did Cornelius Fudge suddenly decide to become a minister?