In 2014, my research group includes four PhD students, me and another professor.
We apply the following process when collaborating on a research paper:
1) In a Google Drive document, PhD student writes a short and rough motivation and if feasible, something that looks like a research question.
2) PhD student shares the document with me.
3) I add comments and edits via Google Drive.
4) PhD student and I meet in person, or hold a conference call, to discuss the rough motivation and research question.
5) PhD student and I identify relevant existing research, and prioritise it.
6) PhD student revises the Google Drive document, by clarifying the motivation, research question, and related work.
7) PhD student and I meet in person, or hold a conference call, to agree on the research methodology.
8) PhD student and I define the research hypotheses, the required tools for collecting data, or otherwise, as required by the research methodology. These are revised usually in several iterations, until I approve that the student can start applying the tools according to the research methodology.
9) PhD student and I (if I can do something more or different than the student can) collect data, do simulations, and so on, whichever is needed. If we need outside experts to help us, we find them and coordinate with them. We clean data up, and decide if it is worthy of analysis, and of what kind of analysis.
10) PhD student shares dataset on Google Drive, along with any analyses of the data, described in a Google Drive document. PhD student and I separately or together analyse data, decide which results to present, and how to present them.
11) PhD student and I decide on the key ideas and results to present in the research publication.
12) PhD student writes first incomplete draft as a Google Drive document. PhD student and I add comments and edit the document until it is approved as ready for submission. In parallel, we decide on publication venue (specific workshop, conference, journal, book chapter).
13) PhD student transfers the content of the Google Drive draft publication, to LaTex format, if this is required by the publication venue. The LaTex files and the resulting PDF are shared in a folder on Google Drive.
14) I approve the PDF version, and PhD student submits it.
The rest depends on the replies from the reviewers at the publication venue.
The process can vary somewhat, depending on the data to collect, if there is data to collect, problems with data, problems with the hypotheses, or the research question, and so on.