How To Get A Complete GNOME 3 Desktop In Ubuntu 12.10, Without Installing Ubuntu GNOME Remix

If you're using Ubuntu 12.10 with Unity or some other desktop environment and want to switch to a complete GNOME 3 desktop experience without installing Ubuntu GNOME Remix 12.10, you can do this by simply installing a few packages.
Using the instructions below, you won't just install GNOME Shell, but also the default settings and applications that come with Ubuntu GNOME Remix. There are also some optional steps to install the GNOME 3 applications which are missing from Ubuntu GNOME Remix.