How far is it from Changsha, and what is the best way to transport there

Do you mean Chengdu? If yes, the distance is about 740 miles.
From Changsha, there are direct flights and trains for you to choose. The duration is about 2 hours if by taking plane.
If taking train, the schedules are 05:32, 14:36, 16:05 and 17:48. It takes nearly 20 hours on the way. You can choose the way you like.