Check first the logs, as seen in desktop/desktop
issue 7690
To access the log files go to the file menu in GitHub Desktop and select Help > Show Logs in Finder (macOS) or Explorer (Windows).
The log files are created daily
desktop/desktop
issue 8516 made a similar request, but the answer was:
This is an interesting idea, but but not something that we will likely tackle in the near-term. I'm going to label this issue as an enhancement and close it out -- if we get further feedback that this would be a valuable addition to GitHub Desktop it may be something we consider in the future.
If you are interested in viewing the specific actions that GitHub Desktop is performing you can open up the Developer Tools by going to the menu and selecting View > Toggle Developer Tools and selecting the Console tab.
You will see the the specific Git commands that are being run, along with other output.
For the most verbose output you can click the All levels dropdown and select Verbose. The log files also provide a historical view of this data, and you can access those by going to Help > Show Logs.... If you have any specific questions about the commands that are being run let me know.