I'm working on an application (hobby project, solo programmer, small-medium size), and I have recently redesigned a significant part of it. The program already works in it's current state, but I decided to reimplement things to improve the OO design.

I'm about to implement this new design by refactoring a big part of the application. Thing is I'm not sure where to start. Obviously, by the nature of a rearrangement, the moment you change one part of the program several other parts (at least temporarily) break. So it's a little 'scary' to rearrange something in a piece of software that already works.

I'm asking for advice or some general guidelines: how should I approach a significant refactoring? When you approach rearranging large parts of your application, where do you start?

Note that I'm interested only in re-arranging the high-level structure of the app. I have no intention of rewriting local algorithms.