What does a graphic designer need to do to monitor the progress of the project?

At first the graphic designer has to break the process down into it's fundamental components. Which could be:

1) Discussion and Clear Comprehension of the Brief
2) Research and Collection of Information
3) Sketching
4) Execution and Experimentation
5) Finalization
6) Revision and Further Corrections
7) Submissions

Then self-analysis is required to figure out the current stage process. Project management soft-wares such as Trello could be helpful when it comes to tracking the progress. Hope this answers the question.

If he tries to grape you then get a grape and grape him back