You can follow the steps from Android Developers documentation about on-device debugging and then inspect the LogCat output.
Thus the easiest way to get log output from your Android device is to install the ADT Bundle (Android SDK + eclipse with Android plugins) from http://developer.android.com/sdk/index.html
Then do the following steps:
extract -> start eclipse -> go to Window>Show View>Other>Android>Log Cat -> connect device via USB.
To filter the log outputs, you can filter for PID or Application Identifier of your game (with level verbose).