Dudhsagar by train
The station that you need is called Kulem, the waterfall is located next to this station, and you need to get on the train either in Vasco De Gama , or at Madgaon station in Margao.
On this route there is a train with frequency, several times a day (like an electric train). But you can get to the regular train that goes from Goa to Delhi, and at the station Kulem makes a stop (you should specify the schedule and find out about the availability of a stop in Kulem).
If you live far away from the Vasco De Gama or Madgaon stations, then the train is not quite convenient, since it is required to get to the station. In addition, the last train from Kulem to Madgaon leaves at 17:00.
The fare on the train is cheap and does not exceed 50 rupees per ticket. If you are going to go to the waterfall by train, be sure to specify the train schedule.