https://developers.google.com/games/services/android/init
The integration is explained here. First you need to import it as a project inside eclipse and then add it to your project as a library.
It also contains the GameHelper class.
if you dont want to use BaseActivity, you can just check out BaseActivity source code and add relevant code to your own activity.
It basically initializes the GameHelper object in onCreate
and call its lifecycle methods in onStart
onPause
etc.
Google itself has guide for it as a separate section here https://developers.google.com/games/services/android/init#using_gamehelper_without_basegameactivity