In my humble opinion, from what I've seen, there is two mostly common approaches. The one is a Best Record share (like mentioned above), even if you have an inbuilt GP leaderboard it's can be a cool addition. The second approach is a link to the Facebook page of your game or you games group, for giving more information about game/s, share more your games or simply gets likes etc. Both methods can be used in Twitter as well. And of course you can download a few popular games from GP with "Facebook button" and just examine it.
P.S I set this Facebook Button in few of my games (Share Record), but I think it's never been used, but my games is not so good and popular so it's a bad example.
P.P.S I just found out that in my builds this "Facebook Share" function is broken Facebook change many things since, so I have no idea how to set this function now.