At http://www.klokantech.com/ we prepared a set of examples for the development with Plovr and Closure Library for newbies. See:
https://github.com/klokan/closure-library-plovr-hello-world-skeletons
There are a helloworld, basic app using Google Maps API V3, a demo with Closure Templates (soy), an OpenLayers app, etc.
I am not sure if you really need to compile modules - especially if you are new to Plovr and Closure. The idea of Closure Tools is that normally the complete code is all compiled into a single .js file - this is the way how the Closure Compiler Advanced minimization runs the best. Read my blog post:
http://blog.klokantech.com/2010/12/closure-compiler-for-openlayers-3x.html
Anyway, the skeleton example code mentioned above also shows how to work with modules in Plovr, eg. dynamically loadable extension of complex JavaScript code - think of a Gmail-like single-page application (SPA) where different parts of the interface are loading additional functionality (such as Settings dialog, Composer functionality for editor, etc). It is in the code as under modules-api
and modules
in https://github.com/klokan/closure-library-plovr-hello-world-skeletons.