I applied through college or university. The process took 1 day. I interviewed at US Navy (Washington, DC)
Interview
2 or 3 technical interviews with engineers. Mostly calculus and physics, but potentially chemistry or technical fields related to the academic concentration of the candidate. FInally, one behavioral interview with the 4-star admiral in charge of all naval nuclear reactors. He will ask questions about motivation, times you've failed (grades below a B), books you've read, etc. Technical interviews last 25-45 minutes each. Admiral interview lasts under 5 minutes and is the ultimate deciding factor in the hiring process.
No interview required. Pre-employment testing is a joke. Be prepared to sign away six years of you life. Great deal of medical screening and superfluous admin required.
I applied in-person. I interviewed at US Navy (Columbus, OH) in Jun 2010
Interview
Went to recruiter, he explained everything, I joined! Make to to ask if you do have questions. Choose a career path before you go in so you can get schooling and make rank.
Interview questions [1]
Question 1
There were really no unexplained things from the recruiter I had. He answered all questions and explained most everything.