Transfer game from one phone to next

[Kelltic]

Hello! I'm new here and not very tech savvy. How do I transfer a game I'm playing from my old phone to the new one? I have an Samsung Captivate Galaxy S and do have an external sd card, I have gone into settings, apps, manage apps, then set the game to sd card. When I load everything onto new phone, (same exact phone as last one if that matters), and dl game from app store, I get a brand new game and no sign of info I've tried to transfer. Thank you for any help you all can give