There's currently a daily build PPA available for the impatient to test things out. For some reason, it shows up as Firefox 6 Alpha 1. Regardless if it's a typo, or it's really Firefox 6, the nightly build is still not something recommended for regular users. Proceed at your own risk.
~$ sudo add-apt-repository ppa:ubuntu-mozilla-daily/ppa
~$ sudo apt-get update
~$ sudo apt-get install firefox-trunk
The nightly build is packaged as firefox-trunk instead of firefox, and it's parallel installable with Firefox 4. Basically, you can have both browsers installed together and switch between them as needed. The nightly build shows up as "Nightly Build Browser" in you applications list.
|Firefox nightly build|
Except for extensions, the browser appears no different from Firefox 4 at this time. It appears stable in the short time I've tested it, but I wouldn't rely on it staying that way. It is a nightly build after all.