A good place to start is the National Park Service's Civil War Soldiers and Sailors database. Enter the info you have on Pierce and look through the search results for who looks like a good candidate. You can reach the database via this link: http://www.nps.gov/civilwar/search-soldiers.htm To start, I normally enter just the first and last names and the state from which the soldier enlisted.
If you have further questions regarding your research into J J Pierce, you'll need to provide some more info such as residence at time of enlistment (county and state), unit if known, etc.