Handling onResume, onPause and onDestroy:

I assume, that you already familiar with Android Life Cycle. Why those methods are considered to be important? Most common purpose for onResume and onPause is resuming or pausing music. 

1. Pausing and resuming music properly:

@Override
protected void onPause()
{
    super.onPause();
    if (this.isGameLoaded())
        music.pause();
}

@Override
protected synchronized void onResume()
{
    super.onResume();
    System.gc();
    if (this.isGameLoaded())
        music.play(); 
}

Where music is your music object obviously. Its important to check if game is loaded by calling isGameLoaded() as an alternative you can also check if music is not null, it will give the same effect, otherwise you can expect NullPointnerException.

2. Destroying activity:

@Override
protected void onDestroy()
{
    super.onDestroy();
        
    if (this.isGameLoaded())
    {
        System.exit(0);    
    }
}

Its important to check if game is loaded, otherwise on some devices, such as Samsung Galaxy S3 (and more devices) game might be immediately closed after trying to open it.