Bobthegrand demonstrates how to clear the search history on the Internet Explorer and Firefox web browsers. In Internet Explorer, click the star on the toolbar to see stored web browsing tabs. Click on the history tab to expose the search history. Right click on the site that you would like to erase and then hit the delete key. Click yes in the verification popup window. In Firefox, click the expandable search options on the left hand side of the browser. Your search history will appear in the window. Click on the site that you would like to delete and click delete. The site will instantly be deleted from your search history.