This post will tell you
Where to find your Firefox bookmarks file on a Windows PC and on a Mac.
How to synchronise your bookmarks if you are running Firefox on several machines
How to backup your bookmarks
How to manually copy your bookmarks to a Firefox on another machine.
Where to find your bookmarks file
Bookmark management changed with Firefox 3. They are now stored in a database in the places.sqlite file in the profile folder. In version 2 your bookmarks were stored in bookmarks.html. You could copy or move that file. In versions 3 and later there are other ways to manage your bookmarks [see below]
Firefox 2 profile and bookmarks file on a Windows XP PC
By default the bookmarks.html file that holds all your bookmarks is in your profile directory. On a Windows XP machine your profile directory can be found at
C://documents and settings/FOO1/application data/mozilla/firefox/profiles/FOO2/bookmarks.html
FOO1 will be your user name on your system. It might be admin or user; depending on how your machine was set up.
FOO2 will be a random directory name generated by Firefox when it was installed. It is different on every installation.
Firefox bookmarks file on a Windows 7 PC
Windows hides your Firefox profile folder which contains contains your bookmarks, passwords etc. You can find it [Google for instructions] but you do not need to do so to manage your bookmarks [see below].
Firefox bookmarks file on a Mac
On OS X 10.5.4 [Leopard]
Your bookmarks [and passwords etc] are in your Firefox profile at
[where FOO2 will be a random directory name generated by Firefox when it was installed. It is different on every installation].
On OS X 10.7.1 [Lion]
In the Lion version of OS X your Firefox profile is in the same place as it was with Leopard but Apple have hidden the library folder. You can get it back by entering the following command in the terminal app provided with OS X.
chflags nohidden ~/Library
The full instructions for this are in this post.
How to synchronise your bookmarks
If the latest versions you can synchronise your bookmarks using Firefox Sync or you can manually copy your bookmarks between machines. I am not going to cover Sync. I do explain below how to manually move your bookmarks between machines.
How to backup your bookmarks
If you are using Firefox sync you do not need to backup your bookmarks file. It is backed up in the Cloud as part of the sync process.
How to manually backup or copy your bookmarks to another machine
Click on Bookmarks and then Show all Bookmarks
Click on icons until you find the drop down menu that has Backup and Restore on it.
You will see that it also has an option to Export HTML. Selecting that will produce a bookmarks.html file that contains all your bookmarks. You can import that file into another instance of Firefox but it is a messy process. Your imported bookmarks and any that were already there are not automatically merged. You have to do that manually and you will find it involves quite a bit of trial and error.
A better option is to select Backup. This produces a .json file containing all your bookmarks. You can manually move it to another machine and import it into Firefox using Restore. Be aware that the restore process replaces any existing bookmarks with those in the .json file. It does not combine the two sets of bookmarks.
You can save the bookmarks.html file or the .json file as a backup.