Locating the record was the hard part (thanks to Ancestry.com I finally managed it) -- I then went onto the NARA web site (National Archives and Records Admin). It isn't the most straight-forward web site in the world, but follow links to military records pre-1917. You can order online then, and pay by credit card. However, I would suggest that instead you download the pdf version of the order form and use it to order NOT the military record but the pension record (this seems impossible to do online). The pension record includes the full military record plus, if the veteran or his widow or children ever applied for a pension or assistance, it can include such things as proof of marriage, etc., which can be invaluable for genealogy. What I got was a copy of the page on which my ancestor was registered, which gave me his age, where born, where recruited from, occupation, and so on, as well as the notes of his service (which is the part I need help with). It also gave a brief physical description, so I know how tall he was and that he had brown hair and gray eyes.
Hope that's helpful!