Prepare the template in advance with the desired design process categories and share it with the design teams/students.
Establish a mechanism to ensure students track their data weekly - for example, send a weekly reminder or request the information in a weekly progress report
Consider the frequency of converting to the design signature visualization. At a minimum, this can be done at the end of the design experience, but then students do not get the benefit of reviewing/discussing their (evolving) design signature. A more recommended approach is to create the visualizations along the way (not necessarily every week, though that would be possible) to enable reflection. The visualizations can be made by the instructor or by the students themselves.
One advantage to having students collect the data on a Google Sheet rather than directly in the DS App is that the spreadsheet is accessible to all members of the team and the instructor. The Google Sheet provides a more permanent record of the data that can later be processed in other ways if desired.