Firefox 3.1 Beta 1 was released on October 14, 2008 and it currently comes in 36 fully-localised languages. This beta is based on Gecko 1.9.1 layout engine and according to the official website, this release features "significant changes to improve web compatibility, performance and ease of use". You can read the release notes on the official website, here.
Debian Lenny comes with Iceweasel 3.0.3, which is actually Firefox with a changed name and a few minor changes. If you have Iceweasel 3.0.3 installed but want to test this new beta without changing anything to your system, just follow the steps below.
Download Firefox 3.1 Beta 1
Get the Firefox .tar.bz2 archive from here, then uncompress it using:
tar -xjf firefox-3.1b1.tar.bz2
Next, move the firefox directory wherever you want it, for example in your home directory, or in ~/apps etc.
Run it using a new profile
Firefox uses the default profile whenever you run it without specifying another profile using a parameter. To run it using a different profile than the default one, use this command after making sure your current working directory is firefox:
./firefox --no-remote -P new_profile
As you can see, we used the name new_profile for our profile. The --no-remote parameter will not connect Firefox to a running instance, so you will be able to run both your current version and 3.1 Beta 1.
Select new_profile (or whatever the name of your profile is) and click on Start Firefox:
You will be prompted to accept the EULA, then Firefox 3.1 Beta 1 will start and you will be able to test it.
A small window should appear prompting you to choose the profile to use. Click on the Create Profile... button, then follow the instructions as in the screenshots below. You will notice you won't even have to close Iceweasel 3.0.3 if you have it running.
Currently there are no available themes for Firefox 3.1, so you'll have to use the default until they are updated.