There seems no direct train from Hong Kong to Changsha, you can make a transfer in Guangzhou. For the train schedule and tickets, you can refer to the China train schedule on this web: https://www.travelchinaguide.com/china-trains/ .

You can cross the border in Lohwu and take a high speed train from Shenzhen to Guangzhou (1 hour; 100 Yuan)from the station just behind the border crossing. Then you take the bus no 3 to the Guangzhou High Speed Train station (1h 15 min, 4 yuan) and then the bullet train to Changsha (2h 30 min, 300 yuan). There are trains every 30 min.

alternatively there are direct flights from Hong Kong to Changsha by Dragon Air / Cathay Pacific. The flight times varies according to the weekdays. The cost is about 2500 HK$ one way.