1. Click the menu button and click over Options.

2. Click on Privacy on the left panel. Select Firefox will: to Never Remember History or if you want to be Granular Use custom settings for history.

3. If you opted for Use custom settings for history click the box for Clear history when Firefox closes.

• To specify what types of history should be cleared, click the Settings button next to Clear history when Firefox closes.
• In the Settings for Clearing History window, check the items that you want to have cleared automatically each time you quit Firefox.
  
• After selecting your options, click OK to close this Window.
• Close the Options tab in the browser, marked as: about:preferences page.