No direct train between them. Shoud transit another train in Wuxi (Jiangsu) or Zhuzhou (Hunan). If taking bus, you should go to Zhongyangmen Bus Station of Nanjing, which has one bus to Changsha at 13:00, and arrived there about 13 hours later. Comparatively, it is a bit cheaper and uses less time than train, but less comfirtable.