By train
Train services run from Riga to Saint-Petersburg (once per day) and to Moscow (twice per day).
There is only one train station in Riga. It is located in the centre of town, 5-10 minutes walking distance from the Old Town next to the bus station and the terminus of fixed-route taxis to Jurmala (Jurmala can be reached by electric train or by fixed-route taxi).
Useful links:
Latvian Railway (LV, EN, RU)