Instructions
Open the PlayStation 3's Internet browser by selecting the small globe icon under the network tab at the main screen of the PS3.
Press the triangle button while in the browser window. This will open up a menu on your right hand side.
Use the directional buttons on your PS3 controller to select the "Tools" option in the menu you opened in Step 2. Press the "X" button to select the "Tools" menu.
Scroll down the "Tools" menu and find "Delete Search History." Press the "X" button to execute the deletion. Note that you can also delete cookies and the web cache from this menu.
Delete the predictive text dictionary by returning to the main menu, selecting the "System Settings" option under the "Settings" tab, and choosing the "Delete Predictive Text Dictionary." Even though your searches have been deleted, the PS3 still saves everything you type into the keyboard in the predictive text dictionary for quick reference. Dump this dictionary to fully erase what you have typed into your PS3 keyboard.