You will need a Firefox Add-on (extension) called Password Exporter, which you can find here. Simply click ‘add to Firefox’ on the page, then ‘install’ on the window that pops up. Then click the ‘restart firefox’ button. Firefox will automatically restart. Then click ‘tools’, then ‘add-ons’, then ‘extensions’. Then click on the ‘password exporter’, then ‘options’, then ‘export’. You may also choose to encrypt the passwords, in which you can use the Master Password you use for the Firefox password manager, detailed here.
Backup Firefox Passwords