This is a question I have been asked many times and answered many times on these pages, but I will answer it again.
You may be able to obtain a copy of your grandfather’s official military service record. Please see this page from the Armed Guard website that I manage: http://armed-guard.com/searchmil.html. In particular see section A.1. Records of Individuals - U.S. Military. You will have to contact the National Personnel Records Center in St. Louis, MO, a facility operated by the U.S. Archives. Provide as much identifying information as possible about your grandfather. The links on the web page above will take you to the necessary pages of the Records Center web site. There will be a fee for researching, photocopying and mailing the information but the Records Center staff will not begin research without informing you of any charge. His military service record would contain such information as dates of enlistment and discharge, the ships to which he was assigned, applicable dates, training, any decorations or medals earned, etc.
Note that someone such as yourself, who is not next of kin to your grandfather, may not be able to obtain his full service record. (Next of kin = parent, spouse, sibling, child.) If there is someone still living in your family who is next of kin to your grandfather, presumably your grandmother, mother/father or an aunt/uncle, it would be best if the request to the Records Center was submitted by that person. You can do the legwork of research, completing forms and otherwise preparing the request but the request should be signed by that person. If there is no longer a person who is next of kin still living, then make the request yourself and hope for the best. There should be something of interest to you if not his full record.
Good luck and best wishes.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website