I applied through a recruiter. The process took 6 weeks. I interviewed at US Navy (Portland, OR) in Jan 2012
Interview
Very streamlined - You are there only to sign your name and answer questions and submit to tests.
Barring some extreme circumstances (disease or arrest history), you will not have any issues with the interview/selection processs. The real test comes with boot camp and training.
Went to MEPS, had a physical, took ASVAB, chose a job, wen to bootcamp, went to a-school, then went to the fleet. Spent 25 years fighting first the communist, then Muslim extremist, and being subject to many social experiments to make us a kinder and gentler Navy.
I applied through a recruiter. The process took 1 day. I interviewed at US Navy (New York, NY) in Jun 2011
Interview
In order to get into the Navy you first have to visit a recruiter. These recruiters then will take you to their local place of enlistment and have you take the ASVAB test. After the ASVAB test are revealed then they let you chose your job in the Navy. The higher your ASVAB test the more job options you'll have.