I'm going to Hengyang from Guangzhou Baiyun Airport probably by train.

If you take the common K or T trains, the closest train station is the GZ Railway Station. You can take the airport express line 1 to reach its terminal at Civil Aviation Ticket Office and then walk to the railway station in about several mintues.
If you want to take the D or G-trains, you need to go to the GZ South Railway Station. You need to take the local subway line 3 to Jiahewanggang Station and then change to line 2 to the South Railway Station directly.