The main.js controller can be accessed in the URL /app/<app-id> , e.g. /app/com.enonic.myapp . We updated the documentation recently. Let us know if anything can be improved.
You can also configure a vhost for the app path to access it in a different URL.
Currently the router does not work from other controllers (service, page, controller mapping). We are working on fixing that, but it will probably require some small changes in XP (not just the router lib), so it would be fixed for next XP release.
There is no demo app using the router yet. But it’s a good idea.
For other people trying out apps in 6.11, I just leave this here: While trying out applications, I noticed that calls to the root of the app and finishing with a slash do not trigger the main.js