Go to the eVetRecs web site (http://www.archives.gov/veterans/evetrecs/index.html), and click on the "Launch eVetRecs -- Request Military Records" link on the right hand side of the page.
This will give you a form to fill out. You'll need your relatives name, date of birth, military id number, ss#, etc.
This form is the same one used to order the DD214. In the comments section, you ask for the service record for the period March 1943 through January 1946. You'll usually get a pile of stuff, and buried in that is usually a small document that shows what ships he was assigned to while in the Armed Guard.
When you finish the form, you will have to print it out, and either mail it or fax it to NARA. Faxing works better (seems to get a quicker response). Don't expect overnight service! Sometimes you'll get a response in a few weeks, other times it takes a few months. You should get an e-mail response pretty quickly saying that they received your request. After that, just wait.
When you ask for the service record, be specific. Tell them he was in the Armed Guard, and you want information on what ships he served on. The easier you make it for them, the more likely you are to get what you want. If you know what Armed Guard Center he was assigned to.
Happy to help more if you get stuck (email me directly at firstname.lastname@example.org, or post here - I check regularly). I have done this many times researching my fathers military records. Patience is the key.