There isn't a interview process for enlisting the in the US Navy. However, throughout your career there are times when you will be interviewed for special programs e.g. commissioning, advance education, and special programs.
Interview questions [1]
Question 1
What would you change if you were the Commanding Officer for a day on a warship?
I applied through a staffing agency. The process took 3 days. I interviewed at US Navy (Memphis, TN) in May 2016
Interview
took an hour and scenario questions on my ability to handle a variety of situations. one phone interview the day prior and a panel of two interviewers for the "in person" interview. it was a back and forth question and answer, delivered from the panel in an alternating basis.
Interview questions [1]
Question 1
Describe a situation where you were required to handle a hostile or angered employee?
I applied in-person. The process took 1+ week. I interviewed at US Navy
Interview
The interview process is pretty straight forward in that to join the U.S. Navy you must simply contact your local Recruiting Office. You must meet minimum requirements such as height/weight. You must also pass the ASVAB which is an exam for entering military service. Recruiters are very accommodating and helpful in explaining Navy life.