A background check, A physical test, An ASVAB test, A Drug Test. If you can pass all that you will be good to go. Not too hard they will try to get you to signup for a rate that needs people, don't settle for this at all.
I applied in-person. I interviewed at US Navy (San Diego, CA) in Oct 2013
Interview
Just go to a recruiting office its easy. You will fill out some paperwork and take an easy general education test. Then you will pick a job and go out for a physical.