Instructions
Turn on your console and scroll right on the XMB menu to the "Friends" section.
Scroll to "Add a Friend" and press "X."
Highlight the "To" field on the "Request to Add a Friend" message and press "X."
Press "X" again and use the controller to navigate the virtual keyboard. Enter your friend's online ID, and press "Enter" and "OK."
Press the "Send" button at the bottom of the message.
Wait for your friend to accept the request.