General developer forum

First of all, dismbiguation of terms:

• A YUI Module is subset of YUI functionality, contained in it's own namespace, e.g Y.Node
• A Moodle Module, I'm sure you understand.
• A Javascript Module in this context, is a subset of javascript functionality contained in it's own M. namespace.

Any Moodle plugin can define it's own Javascript Module, whether it's a Moodle Module or a different type of plugin. Usually this will be in the plugin's module.js file, and be called M.plugintype_pluginame (similar to the lang file naming convention), but the object passed as the 4th parameter of $PAGE->requires->js_init_call() allows you to customise this.

The best example (i.e. the one I'm most familiar with) of Y's usage that I can point you to is my quickfindlist block.

Take a look at the bottom of get_content() in block_quickfindlist.php. This defines $jsmodule (the Javascript module's parameters, including the name, the file it's stored in, and the YUI modules it needs), $jsdata (extra parameters to pass with the init call, in addition to Y), and then passes them, along with the name of the module's init function, to js_init_call(). Note that as it's a block, it uses $this->page in place of $PAGE.

Now look at module.js. It defines M.block_quickfindlist (which is the module we specified with $jsmodule) and the init() method (which we referenced in js_init_call()).  init accepts 6 parameters: Y, and the 5 set in $jsdata.  It then stores a copy of Y in M.block_quickfindlist.Y so it can be used in other methods, and uses Y itself to call Y.on(), adding event listeners to the block.
M.block_quickfindlist.search() is defined futher down module.js - it needs acces to Y too, so we create a copy in the method's scope for easy referencing, before using it to make an AJAX request with Y.io().  You can also see use of M.cfg, another Javascript Module, to access the value of wwwroot.

An important thing to note about Y being used all over the place is that as I understand it, Y is only initialised once with all the YUI Modules required by any Javascript Modules on the current page (hence the requirements manager). It's then passed to each module's init function, so they can use it in their own scope.

The actual "core" javascript code to do this would look something like:

YUI.use('required', 'yui', 'modules', function(Y) { 
    // YUI.use initialises Y with required modules, 
    // and passes it to an anonymous function.
    // Y is then available to pass to our own init functions
    M.block_blockname.init_function(Y);
    M.report_reportname.init_function(Y, other, parameters);
});

Hope that's answered at least some of your questions