Instructions
Open the Playstation 3's Internet browser by navigating to its icon in the network section of the cross media bar and pushing "X" on your game controller.
Press the triangle button on the face of your game controller and navigate to the "History" menu.
Press the triangle button again and choose to "Delete All."
Highlight "Yes" when you are asked if you wish to continue and push "X" on your game controller. This will cause the Playstation 3 to delete your search history.