The trip from Riga to Valga will take about 3 hours, and the ticket costs LVL 2.29 one way. You can also pay in Estonian kroons (54 EEK for Riga - Valga).
It is planned that in the future the train will go to Tartu and Tallinn. It is not possible at the moment because of the reconstruction works between Tartu and Tallinn.
According to Latvijas dzelzceļš, this is an important step for the project Rail Baltic.
Attention! Please note, that even though after the adoption of the Schengen treaty you can cross the border without passport, the authorities still have a right to demand you a valid form of ID!
More information about the time schedules: http://www.1188.lv/satiksme/vilcieni/