If you have bookmarked many websites in your Mozilla Firefox and want to take backup of those saved bookmarks to your computer directly from your Mozilla Firefox browser then you can do this in few steps and in future if you want to import those bookmarks back to your browser then also you can import those bookmarks and you can use it. Means by this method you can take backup of your favorite bookmarks and in future you can use it at any time.
I have used Mozilla Firefox browser 3.6.8 while preparing this post. In other versions, the positions of Export and Import buttons can be found at other locations in menu bar.
How to backup the bookmarks of Firefox to the computer
Open Your Firefox Browser. Then Go to Bookmark tab. Then Select Organize Bookmarks option as shown in the following figure .

Once you have clicked on Organize Bookmarks option from the Bookmark Menu bar then it will open the Library of bookmarks in a popup window. Select All Bookmark Option from the left side bar as shown in the following figure.

After you have selected All Bookmark Option in Library then see at the top bar in Library, you will see Import and backup drop down button. Now, Select that button and choose Export HTML option as shown in following figure.

Now, You have to save this bookmark. You can write any name for that file and save it on your hard drive.
How to upload Firefox Bookmark Backup to Firefox browser
As You have selected Export button from the Bookmark Library, same you have to do but now at this time you have to click on Import Button from that Drop Down Option. So, Open Firefox Browser, Select Organize Bookmark Option. It will Open bookmark Library. See the Import and backup Option on the top and finally select Import HTML Option as shown in the following figure.

Now, It will Open a import wizard window box. You have to select the second option from the HTML file and click on next button as shown in this figure.

Now you have to choose the location to upload that HTML file as shown in the figure below.

Select the file and click on open button and finally it will upload all your bookmarks to your firefox browser.
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Thanks for the information that tells about the Firefox details, though in addition to it, we can take a backup of everything regarding Firefox Like Bookmarks, Passwords, Favourites, Profiles etc. even Backup of Firefox itself too.
We can also use a free service like Xmarks to backup and Synchronize the Bookmarks in all the Browsers..