Like with many things in life, you can get people to do things that you want them to by offering an incentive. Any parent knows how to use positive reinforcement with their children – “once you finish your homework, you can watch a show on television”.
And the same works when you want to get more fans on your Facebook page – offer the visitor a deal or some content that is only available to fans.
This can be done with an fbml tag called visible to connection.