How do I transfer my Game files?

Hello, i lost my itouch last year, and had very fun games like Snoopy's Street Fair and Cut the Rope. Now, i got a new 4th generation itouch, and wondering how to transfer my cut the rope accomplishments to my new itouch so i don't have to start from the beginning. Fortunately, the accomplishments are on my Game Center, and i do have some of my old apps on my itunes.. However, i don't know how to sync it. Help?