That's a good question because I am working on one like that myself. If his serial number is ledgible, and you know which branch of the military he was in, you may be able to get some information from the National Archives. There's a standard form 180 prescribed by the NARA:

http://www.archives.gov/research/order/standard-form-180.pdf

Just fill it out and send it in. Unfortunately, my GG father's serial number is illegible and I don't know for sure which branch of the military he was in.

Be aware there was a fire in St. Louis which destroyed much of the military's WW I records. If you can't get anything from NARA, you have to start getting really clever. Some of the states kept their own censuses and other records on WW I veterans. There are also some regional NARA archives of docket books and other records that were kept by the local draft boards. These are volumes of printed material. The one I found which pertains to my research is record group 163, 283 cubic feet of printed material:

http://www.archives.gov/great-lakes/holdings/rg-100-199.html

I will research that only as my last resort. Good luck.