This screen is relatively straightforward.  Note, though, the somewhat unusual hotkeys - Alt+5 for Senior, Alt+6 for Distinguished Senior, and Alt+$ for Press.

Classification dates are normally maintained by the system each time you commit a Classifier.  

 

They appear on the main shooter list when you opt to sort by last Classifier date:

If you want to update them manually, click the Unlock Dates button.  These dates come into play when you are registering shooters for a sanctioned match.