This is mostly for Jon and Ryan since they're likely to be working on other parts of references in VE in future or at least reviewing corresponding code. I've just asked James how to set up references on my dev instance and it's a bit more complicated than I expected. This might slow me down on the first references story a bit. I'm posting what I know so far so that others can update their dev instances.
First of all, for the Cite menu to show up even in desktop VE you need to create MediaWiki:Visualeditor-cite-tool-definition.json page with the following content (default for enwiki):
[ { "name": "web", "icon": "ref-cite-web", "template": "Cite web" }, { "name": "book", "icon": "ref-cite-book", "template": "Cite book" }, { "name": "news", "icon": "ref-cite-news", "template": "Cite news" }, { "name": "journal", "icon": "ref-cite-journal", "template": "Cite journal" } ]
Now you have the Cite menu in the toolbar in VE, but the dialogs don't really let you do anything. You need to use Special:Export/Import to import those templates (Template:Cite web, Template: Cite book, etc.) into your local dev instance. Unfortunately, those templates require Scribunto. If you don't have Scribunto installed in your local instance, it might be a good moment to consider a move to mediawiki-vagrant (which is what I probably will do).
It will probably take me at least a couple of days to come up with something for code review, but the sooner you get this working, the better.