There are technically 4 summer training blocks, each about 3 weeks long (except for Block 0 which I will explain below).
Block 0 is a special training block mostly meant for varsity athletes that have to come back to the Academy early before school starts for sports practices. It starts right after finals week finishes and ends right after Graduation. This time is more commonly know as Intersessionals, which everyone gets off, and Dead/Commissioning week.
The rest of the training cruises follow in order (Block 1,2,3) at about three week intervals, which Block 1 starting right after graduation. Midshipmen typically have two summer training blocks and one block of leave.
As a side note, some midshipmen get selected for Block 0 training even though they may not need it. They then do another regular block of training, and get two blocks of leave.
If you don't have Block 0 training, you are on leave after your last final for about a week or so. It's basically like another Spring Break...Kinda...Then you come back for Dead/Commissioning Week. During this time, there's not much to do except pack and clean up your rooms, plus march in a few parades.
Major events of Dead Week include Sea Trials and 2/C Ring Dance. Commissioning Week involves lots of parades and then everyone goes to the graduation ceremony.