Based on ASVAB store, need to take an ASVAB at a local recruiting station and based on the score will determine qualifications but job availability will also be a factor.
I applied in-person. I interviewed at US Navy (Berwyn, IL) in Oct 2011
Interview
All you have to do is to go through your local recruiting station. You talk with the recruiter to determine your interests and duration of your enlistment. Typically you get the most benefits by signing up for 4 years.
I applied through a recruiter. The process took 5 months. I interviewed at US Navy (Washington, DC) in Dec 2011
Interview
Medical screening, over-the-phone interviews, technical interviews, and interview from the Director of Naval Reactors. This was about a five month process. The medical screening was fairly intense and there are many dis-qualifiers. There were two technical interviews about 45 minutes in length. The interview with the director was about one minute. Results were received shortly thereafter and you are sworn into service that day. In the Nuclear Propulsion Officer Candidate Program (NUPOC), you enter the service enlisted and then commission when you complete your Bachelor's Degree.