There are only 2 files you need to backup:
- signons.sqlite
- key3.db
You can find those in your Firefox profile:
Linux
~/.mozilla/firefox/xxxxxxxx.default/
Windows
- Click the Windows Start button, and select Run…
- Type in %APPDATA%\Mozilla\Firefox\Profiles\ then click OK.
You can then copy those file to another computer in your Firefox profile to use them.