By default, Firefox remembers your browsing history to make it easier to return to a visited site.
Select Options and then Privacy in the left hand navigation panel. Under History, open the drop-down menu labeled “Firefox will:”and tell the browser to never remember your history or use custom settings.
Selecting “Always use private browsing mode,” is for hardcore privacy, but you need to understand the implications of private browsing mode. See the Mozilla’s support pages for more information on this.
Here are the History settings that I suggest.
Uncheck the box for remembering your browsing and download history, un-check remembering search and form history, and leave the box checked for “Accept cookies from sites.” Then under “Accept third-party cookies” set it as Never, but change “Keep until:” I close Firefox. Finally check the box that says “Clear history when Firefox closes.”
This combination of settings allows Firefox to behave normally, but erases most of your activity upon closing the browser. These settings provide some measure of privacy without sacrificing functionality.