For Cause and Comrades: Why Men Fought in the Civil War - James McPherson. McPherson is one of the leading scholars on Civil War history, and this book is, from what I've read, the best general introduction to this topic, although it does cover the Union as well.

Most books published on this topic tend to focus on specific regions, demographics or specific parts of the militaries. It is easy to find a good book on the experiences of Confederate sailors, or raiders, or Confederates from Tennessee or Texas, etc. To my knowledge, there's no single book which comprehensively anaylses the experiences of soldiers in all theatres and units. In that regard you might be well off reading a general history of the war as well.