You or other next of kin (spouse, sibling, child) members of your family should be able to obtain the military service record of your father. See this page from the website I manage: http://www.armed-guard.com/searchmil.html, in particular see section A.1. Records of Individuals - U.S. Military. This provides details about requesting a copy of your father's service record.
The service record should include such information as:
* duty stations and assignments (including the names of ships to which assigned)
* training, qualifications, performance
* awards and medals
* applicable dates for any of the above
* other personnel actions
This will all be kind of dry administrative stuff and not personalized or memorable as would your father's stories, had he told you any. On the other hand, information in the service record may provide leads to other sources of information about your father's service. For example, many major warships have crewmen's associations (alumni organizations if you will) for men who served on these ships. These associations often have newsletters, websites and reunions, any of which may be a gold mine of information for you.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website