Overview - Tracking progress and recording completion are essential parts of doing research. There are two aspects involved here:
1) Progress and completion in the lab: Is your mentee properly trained on all instruments? If not, what is the next step and how do you know they are ready?
2) Data progress and completion: your mentee should be trained on the importance of keeping a clear and thorough lab notebook, as well as how to properly analyze their data and log that into their notebooks.
This step of the process is research group-dependent, so each group does it differently. If your PI does not have a set of rules to be followed in this case, think of things that are important to you, and how you track your progress in the lab.
Let your mentee know how your group tracks progress: group meetings, one-on-one meetings with PI, formal presentation of results, maintaining a lab notebook, etc.
There are probably sets of experiments or a specific instrument in your lab that can be used to test the mentee’s knowledge/level of understanding.
Example: Have them perform an experiment that is a standard in the lab and compare their results with yours. If they get it right, they can now start trusting their technique, and if something ever goes wrong, they can start thinking about how to troubleshoot/solve that problem.
With some research groups, such as organic synthesis, it is easy to track progress (a correct product and excellent yield are good indicators of success). Try to find what works for your lab.
Another strategy can be having a mentee creating an exhaustively detailed SOP (with figures, pictures, charts, etc.) and having that edited by the mentor. This can not only cement knowledge in a mentee's mind, but can also secure this knowledge for the next person who will be involved in the same research.
One note when it comes to lab notebooks: Do not forget to tell your mentees that their lab notebooks are property of NC State University, and therefore it needs to be properly maintained and returned to the lab once their research is completed.