Yours is a pretty broad question, so I'll try to answer parts of it:
Q How can I get service selected into subs from USNA?
A Each service area has factors that are critical, and for subs, academics is the most critical area. Every sub officer must pass "nuke school," which is a tough course heavy in nuclear physics. On top of grades throughout the four years at USNA, sub selection candidates must pass a rigorous set of interviews. If my Mid's interviews are representative, they include a series of technical/scientific problems which must be solved and explained to the interviewer on the spot. There's also an interview with the Admiral in charge of the Nuclear Reactor program.
Q What training happens after Commissioning?
A. Naval Nuclear Power School (NNPS) (nuke school) 24 weeks
Nuclear Power Training Unit (NPTU) (prototype) 26 weeks
Submarine Officer Basic Course (SOBC) 12 weeks
http://www.navy.com/careers/nuclear-energy/submarine-warfare-nuclear.html
The following link has a lot of general question/answer that might be more what you're looking for. The only error I noticed is that women officers are now being trained to join the sub community.
http://usmilitary.about.com/od/navy/l/blsubfaq.htm