There is some changes in how Game Center will work with IOS8.
First of all if you want to test Game Center you need to enable sandbox mode on you device. To do that open Settings app, scroll down to Game Center, and enable Sandbox mode under the Developer settings:
After this you can test Game Center with your game.
If for some reason game center steel not working event with sandbox enabled.
Make sure you created you app correctly and building it with correct bundle id and provision profile.
Make sure that sandbox mode was eventually enabled on device. Open Game Center App, and you should see sendbox mark like on the screenshot below.
Read more about how to use Game Center API with IOS Native here.