Some basic questions about creating a webform handler from the module webform_example_handler
Could someone please tell me what key thing(s) I need to do to make
  that connection


There are 4 ways that you can tell Drupal that your plugin exists. 

You can read about the other 3 at D8 Plugin discovery

In this case Webform uses:


  AnnotatedClassDiscovery 
  
  The AnnotatedClassDiscovery class uses name of the annotations that
  contains the plugin definition, e.g., @Plugin, @EntityType, in plugin
  docblocks to discover plugins, minimizing memory usage during the
  discovery phase. The AnnotatedClassDiscovery class takes an argument
  in its constructor, $subdir, which specifies the
  sub-directory/sub-namespace for this plugin type. The
  AnnotatedClassDiscovery class scans PSR-4 classes inside those
  sub-directories of Plugin folders to find plugins (see a
  "Annotations-based plugins").


Side Note: Entities and blocks also use this "annotation" method.

This "annotation" is seen in webform_example_handler/src/Plugin/WebformHandler/ExampleWebformHandler.php



Yes, this info is inside a comment block, weird, but that's just how it works.




  In webform_example_handler.schema.yml the first line is:
  webform.handler.example. Is this a standard Drupal construct of
  &lt;webform&gt;.&lt;handler&gt;.&lt;my_module&gt;, or something specific that must be
  followed set by the webform module or am I completely off base on how
  this is derived?


Wrong, otherwise it would've been named webform.handler.webform_example_handler. 

It's actually webform.handler.&lt;WebformHandler_id&gt; (The ID you use in the annotation).

This is because your module can have multiple plugins, so it makes no sense to use the module's name here. 



The webform.webform.webform_example_handler.yml file: could someone explain the parts? In my module would it be: webform.webform.dis_doc_gen.yml ?

Assuming your module is named dis_doc_gen, correct.




  Last: I have built my webform through the interface so I assume that I
  don't need the file webform.webform.webform_example_handler.yml as
  that would only be for creating a webform from a yml file upon
  installing the module as far as I can tell


Correct, anything inside the /install folder, runs on install and that file is creating a form. Since you created one via the UI, you don't need this in your use case.