Nathan, you must add the "ricotz" PPA to get GNOME 3.4.
But I have mentioned it before, using that testing PPA some things might
break. When I tried it the Trisquel theme broke and I could no longer play
Flash videos in the browser using the default settings. Those were the only
problems I was aware of. There could be more, or maybe those are the only
things that break. Make sure you know how to undo a PPA if you want to test
this on a production system.
The theme problem is easy to solve if you select another theme, like Adwaita.
I didn't look for a solution for the Flash problem, but if you use something
like Linerna Magica it should not be a problem.
Please refer to this old thread:
http://trisquel.info/en/forum/how-run-gnome-shell-and-use-most-recent-version
(The steps are in the bottom post).