With some basic information about your father, you can find out where he served during his time in the service. Start with the Standard Form 180 and fill in as much information as possible, then, submit it online. Several questions come to mind about your quest: Is your father living? Do you know his military service number? Do you know his place of birth? Do you know in which branch of the military he served and when?
In addition to the online form to request military records, you might Google the name(s) of any ships where he was stationed. The online administrator can direct you to personnel lists. Do you know any duty stations where someone might remember him? Perhaps they have a list of assigned personnel by year.
Another option is to Google the online site for National Archives where they have a "Contact Us" option.