There is no subway in Hainan Island, only the high-speed rail around the island. You can buy it through 12306 or go to the railway station to buy tickets. There are many flights every day.
Sanya station takes the train to Haikou, Haikou East Station.
Haikou stands on the west coast of Haikou, and Haikou East Station is in downtown Haikou. Please read it carefully when you buy the ticket.