I have already built a site with backbone marionette and now I am trying to use Google Tag manager to add the tracking. But I have no idea how to configure GTM, in order to listen page change and button click event.
Clicks are up to you to set up listening events and track manually from views. Page views can be tracked like this:
Backbone.history.on('route', function() {
// Send Backbone.history.fragment to your page view tracker
});