Hopefully you have his WW 2 discharge certificate. That should give you his service number and assignments. If not, ask family members if they may have a copy. You can also check the tax office or town clerks office in the town/city he lived in to see if they have a copy. Many veterans place a copy of their discharge papers on file for tax purposes and safekeeping. Have you checked the Navy muster rolls on Ancestry for his name?
Here is the information to request his personnel records from the NARA Archives in St. Louis.
http://www.archives.gov/st-louis/military-personnel/How to replace ribbons/medals-
http://www.archives.gov/st-louis/military-personnel/public/a...