Perform the find on a layout based on TrainingSignatures. Specify the course name in Trainings when you perform the find for all people that took a particular course.
This can be a manual find if you put the Course Name field from Trainings on the layout. This type of search can also be scripted.
If you set up the layout as a list or table view, you'll be able to either get a list of all courses taken by a single person or all people that took a particular course--depending on the criteria you use in the find.
If you want to script this process, you might find the examples found here to be a good source of ideas: Scripted Find Examples