Click on the "Account" link (upper right), then click on "Manage All Friends," pick the Friend you wish to remove, scroll down and click the "Remove Friend" button.
Storing this in cookies/session is the way to go. In PHP you can just use the $_SESSION functionality to do this. More info on that here.
This will not work if the user opens a private browsing session, though. IP tracking would work, but IP addresses change due to ISP assignments and may represent different users (for example, two users in one home sharing the same DSL connection). For these reasons this is not recommended.
Best Answer
Removing a friend is listed in their FAQ: