First, now we all live in an age of advanced information technology: try to find information on the Internet. If you know the military part number, enter it in the search engine. As practice shows, now in almost every part has its own group on social networks, you can easily find by ID number. And then, as they say, a trick. On the forum the local "old-timer" ask if they know of such a person, and if so, where and how they served together.
If the Internet did not help, proceed to plan "B". Each soldier, after demobilization obliged to put a mark on military service in the army in the military at his residence, where he was drafted into the army. Then he is obliged to provide accurate data on the place and time of military service, branch of service, military unit number, exact address. So the easiest way to find the information you need is to contact the military.
If you have only approximate information about the location of the service personand, for example, County or area then you will have to do hard work. Make or find (in the Internet) a list of all military units of the area with exact addresses and phone numbers. Then call and request the information you need. Of course, not the fact that you are willing to provide, but the chance still remains.
The ideal option is a special request from law enforcement or prosecutors, but this is usually required if the person is on any criminal case as a defendant or witness. You do this information can only be obtained indirectly, either as a part of the person or having been in open court.