First of all you will have to sign up for access to the service. You can do this from Googles sign-up page.
You will then have to enter the Google account id into the Constants class where you will find a constant called named C2DM_APPLICATION_SERVER_ID.
The application is using the Maven build system, utilising the maven-android plugin. This makes it very easy to build and install as long as you have Maven installed. You will need to connect your Android 2.2 device or start the emulator, then issue the following command in your shell:
$ mvn install android:deploy
For the device side this is pretty much it. When you have set up your server you can go ahead and start the application. You will be presented with a button which you click to register for receiving messages. When you then use the server to send a message you will see this being printed to the log.