If you want to conceal your recent activities and clear your browsing history in Mozilla Firefox, this guide is exactly what you need.
Steps
Firefox 2.6

Click on Firefox. Once the program opens, click on the orange Firefox button located at the top left corner.

Hover over History. A menu will appear when you click on Firefox. Hover over History on the right side of the menu.

Click on "Clear Recent History". This will open up options to delete.

Select the time range. Choose the time period from which you want to delete history.

Pick the items to delete. There are several categories you can clear. If you just want to make sure no one knows what you've been up to, delete four items: browsing history, forms, cookies, and cache.

Click on "Clear Now". And that's it, your history is cleared!
Firefox 4

Click on 'Tools' in the Firefox menu.

Click on 'Clear Recent History'.

Check the boxes next to the items you want to delete.

Click on 'Clear Now'.
Firefox 3.6 and Older Versions

Launch Mozilla Firefox.

Open Firefox Options (Tools > Options).

Click on the Privacy tab.

Click clear your recent history to delete your browsing history.

Select the time range you want to clear. If you wish to delete all your history, choose Everything.
- If you select Everything, make sure to check all the options.

Click Clear Now to delete.
Click Ok.

Restart Firefox.
Tip
- If you're using a shared computer, make sure to clear your recent history after each session.
Warning
- Once deleted, your history cannot be recovered unless you perform a system restore.
