Brenda,
I would suggest you first look at the index of Tennessee Civil War Soldiers at www.researchonline.net/tncw/page5.htm and you will find two James C. Maynards, one with the Union 9th Cavalry, Company C, and one with the Union 5th Cavalry, Company I. Federal (Union) rosters are at www.tngenweb.org/civilwar/rosters/ . That will get you started. Post any further questions you have and someone will be able to help you.
Ray Walters - Independence, MO