You can find it by scrolling to the bottom of your game. You'll see a small section of gray text that will read like this: "User ID: 100001524941586".
If you do not see the user ID/Facebook ID written at the bottom of your game, you can find it by looking at the link to your Facebook profile:
Your Facebook User ID may be the last number after the = in your URL. For example: http://www.facebook.com/profile.php?id=100001224446821
If you have a custom user name (e.g. Zuck) replace the “www” in your profile link with "graph". For example: http://graph.facebook.com/Zuck. Click the graph link and you’ll be taken to a page that shows your Facebook User ID.