This has been an ongoing process for the past 3 years that started with me learning org-mode to manage my todo list. Most of my students have taken a class with me, where they already had some familiarity with emacs, and in which I use org-mode for the assignments. Some of them took to it like fish in water. A few have not drunk the water, and are thirsty as a result ;) For track changes, I use git, and look at diffs when needed.
I have had to train my students to prepare simple documents, e.g. org documents, that grow in sophistication over time. I generally provide a lot of support for this, through my blog (
http://kitchingroup.cheme.cmu.edu[kitchingroup.cheme.cmu.edu]), and in meetings. I am certain my students are tired of hearing answers to their questions that start with "I wrote a blog post that explains..." But they probably realize they get faster and better feedback when they send me org docs. I am working towards a set of emacs packages for my group that will streamline manuscript preparation, and communication.
For file sharing there are two main approaches we use. 1) Part of my group is computational and we all have accounts on a shared cluster. We share some documents there. 2) PArt of my group does experimental research. We use Dropbox too. I have a folder for each student that is shared with them. Each student has an org-file that outlines their current research projects and priorities. We use this document to guide our meetings. These documents are on my agenda list so I know what should be done and by when. And the students know it too. This is also how we coordinate manuscripts.
Manuscripts are a primary learning experience. Our supporting information files are routinely 20-100 pages long now because I make my students put comprehensive detail about what they did in them. Partly so I can be sure of what they did, and partly for others to learn from.
So, it is still ongoing. The only alternative I am offering my group to org-mode is LaTeX. They usually make a wise choice ;)