First create an InputProcessor to handle the back key actions and then add it to a multiplexer so that other components still receive similar events.
InputProcessor backProcessor = new InputAdapter() {
@Override
public boolean keyDown(int keycode) {
if ((keycode == Keys.ESCAPE) || (keycode == Keys.BACK) )
// Maybe perform other operations before exiting
Gdx.app.exit();
return false;
}
};
InputMultiplexer multiplexer = new InputMultiplexer(mStage,
backProcessor);
Gdx.input.setInputProcessor(multiplexer);
And enable catching the back key.
Gdx.input.setCatchBackKey(true);
That's all there is. Good luck!