This answer is outdated. As of 2020 / Xcode 11.4 it’s now possible to test push notifications in the simulator
See this full explanation in an answer below
Sorry to say, but you’ll need to find some hardware to test this functionality.
Push notifications are not available in the simulator. They require a provisioning profile from iTunes Connect, and thus are required to be installed on a device. That also means you’ll probably have to be accepted into the apple iPhone developer program and pay your $99.
On the bright side, with the iPhone OS 3.0 update, you can test this functionality on any device, including the first gen iPhones.