It can be very difficult to find personnel information on World War II veterans. However you can write to the National Personnel Records Center located at 9700 Page Boulevard, St. Louis, Missouri 63132.
You will need to have the following information about your relative: name, date of birth, and home address in 1941. If they can locate your relative's record, they will send you a service record with unit numbers. Once you have the unit number, you can research the history of the unit.
Unfortunately there were an untold number of military records that were destroyed by a fire in the St. Louis depository, which reduces the chance of finding the information, but hopefully you will be one of the lucky ones. If your relative was wounded and hospitalized there is also a chance that the Veterans Administration would have some records.
Operated by the National Archives is "eVetRecs," an online service to request personnel information from your, or your relative's, military personnel records. Please be aware that in order to request information about a relative, you must be their next-of-kin.