Install GNOME Shell along with the GNOME3 core applications:
# apt-get install ubuntu-gnome-desktop ubuntu-gnome-default-settings
When prompted, select GDM as the default display manager.
If you already had GDM installed and the package manager didn’t prompt you to choose between LightDM and GDM or you’ve selected LightDM by mistake, you can run the following command:
# dpkg-reconfigure gdm
You can use LightDM with GNOME Shell, but you won’t get the complete GNOME 3 experience - for instance, GNOME Shell won’t use the new GNOME 3.6 lock screen. It is also a good idea to remove the “ubuntu-settings” package:
# apt-get remove ubuntu-settings
Note that removing this package, the “ubuntu-desktop” package will be removed as well. This is just a meta package and your system shouldn’t be affected by it. The “ubuntu-settings” package is used to set various Ubuntu defaults, like the window button order, which Rhythmbox plugins are enabled by default and so on.