You can sign in and access Game Center details within iOS Settings:

Once in Settings scroll down to the section that says "Game Center" and tap on it:

If this is your first time accessing Game Center or you have previously signed out, tap on "Sign In", and sign in with your existing Apple ID. NOTE: If you've connected Dots & Co to Game Center before, you must use the same Apple ID in order to successfully retrieve and continue to sync your progress:

If you are already signed in and need to disconnect/reconnect, tap your e-mail address on this screen and tap on the sign out option, after which you should see the option above again to "Sign In".

You can sign in and access Game Center settings via the Game Center app: