For Navy records you might start with these sites. I just googled "finding us naval personnel records" and got these, among others. there are lots of "paid" services out there, but I think you might be able to start with these and get a little further along without paying for it.
The US Navy Frequently Asked Questions
Finding US Navy Records and Drawings
[Research Guidance: U.S. Military Records - Research Outline] Research Guidance Version Of Data : 6/9/2001
For civilian family members,
Ancestry.com is a good place to start.
Good luck!!