Promote Facebook App With Like Gate

Hey I have an App which I use for my fan-page - it has a like gate and you can win a cool prize.

can you give me some tips how to promote the App so I get more users?

At first glance it seems a daunting task to promote facebook apps but I know folks that drive huge traffic to them. I think finding the cheapest (if not completely free) traffic source is the way out. Suggestions from more experienced members here will be appreciated