The train station is located about 15-20 minute walk outside of the town center. Szabolcs Volán (http://www.szabolcsvolan.hu/) runs bus service throughout the city and to small villages in the region as well. Nearly all the buses from the train station except #6 and #16 run through the city center. If going to Sóstó, Bus #8 but not #8A leaves from the train station and town center.
All tickets can be bought from any newspaper kiosk or from the driver at an additional cost.
Another option for going to Sóstó from the train station is to take the narrow-gauge train departing from in front of the train station. This train is something like commuter rail to Sóstó, however, it doesn't run nearly as frequently as the buses.