Here's the link to the summer schedule:
http://www.usna.edu/acdean/calendars/130.pdf
It shows when the training blocks begin and end. Not shown is zero Block, but that is typically reserved for varsity athletes and usually begins just after final exams and extends to the beginning of Block 1.
As for the actual training, my now-Youngster was a trainer for NASS during Block 1, then took a voluntary summer school class for Block 2, then assigned training cruise during Block 3. Voluntary summer school is worth it if you want to have more flexibility in taking elective courses during the ac year, double-majoring or doing a minor in a language. If you don't do summer school and you are not academically unsat (and therefore might have mandatory summer school), you can have a fairly significant chunk of leave to go home or do something else fun during the summer!