A video tutorial is available here.
Updating the viewer, either upgrading or downgrading, implies more than just uninstalling or deleting the viewer and then reinstalling it. Doing that leaves behind all the settings and would only fix problems with the installed files. Updating, therefore, also includes manually locating and deleting all your settings and possibly cache files.
For troubleshooting, you may need to delete just your settings, or just a portion of your cache. Troubleshooting steps leading to those procedures are here.
If you save chat transcripts, they are by default saved in your per-account settings folder (named for your avatar). Before you delete that folder (below), you will need to identify the chat files and move them. See here for steps to relocate your chat transcripts. This only needs to be done once if you then backup your settings. But you must log in on each account (i.e., alts) to save that account's chat files.
As a just-in-case measure for any situation, and to make upgrading or downgrading your viewer much easier, make a backup of your settings. You must log in on each account (i.e., alts) in order to back up that account's settings.
REMINDER: If you want to save chat transcripts and or settings, make sure you do Steps 1 and 2 before deleting your settings.
Firestorm settings can become corrupt, particularly if you recently crashed; the files may not save completely, so important information can become “scrambled”. And when installing a different version of the viewer, using settings from the previously installed version may cause undesirable behavior in the viewer. For these reason, wiping your settings, while “painful”, may be necessary. Here is how:
*Note that the Firestorm folder name may differ slightly.
Note also that if you have both a 32-bit and 64-bit version installed, you will only be deleting settings for the version that you launched at the beginning of this step. You would have to repeat this step if you want to delete settings for the other version that's still installed.
Clearing cache should only be done when there is a problem with the cache, or when there is a significant change in the viewer that requires it. The Firestorm downloads page will advise you when clearing cache is needed for installing a specific version.1)
If you have to clear cache in order to use the viewer version you are about to install, please see this page.
Ideally, use the Programs & Features Control Panel [Vista, Win7, Win8], or Add/Remove Programs Control Panel [XP] to remove the Firestorm application. If you have a Firestorm folder in your Start Menu, there may be an Uninstall link there (32-bit Firestorm only).
Navigate to Applications and trash the Firestorm App.
The Firestorm install directory will be wherever you extracted the download archive. Typically this will be in your home directory somewhere, such as ~/Phoenix-Firestorm_*. Delete this directory and everything inside it.
If you used the install script as root, look in your /opt directory. You will need to su root or sudo rm to delete the firestorm directory there.
Having done all those steps, you may now install Firestorm. Installing Firestorm is done in pretty much the same way as any other application on your computer.
Run the downloaded installer. The 32-bit installer will offer you the chance to change the destination directory; the 64-bit installer shows the destination when you click the Options button.
The installer will create a shortcut icon on the desktop.
Note: Choose No if you are prompted to start the viewer.2)
Find the .dmg file you just downloaded and double-click it to mount it. Then drag the Firestorm app icon into your Applications folder. More detailed instructions can be found here
Extract the downloaded tar.bz2 or tar.xz into any directory and run the firestorm script inside that directory to launch it. You can optionally install by running the install script inside that directory. And you can optionally create a desktop launcher. Refer to the README files for more information.
If installing the 32-bit version of Firestom on a 64-bit version of linux, refer to this page for guidance on required compatibility libraries.
Some Ubuntu users may need to modify how Nautilus handles scripts.
Once you have the viewer installed or reinstalled, you will want to make sure the viewer is operating correctly:
At this point, if the viewer is performing as it should, you can restore your settings and again relog. You must log in on each account (i.e., alts) to restore that account's settings.
Log back in to SL once again and confirm that the viewer is still performing as it should; then you can adjust any new or changed settings and then back those up.
Note that some settings are not restored, such as graphics. This is because the graphics settings could be incorrect and may cause problems.
See this page for documentation on Firestorm 4.6.9 (42969) and earlier.