You can take bus K300 directly from South Hangzhou Railway Station to Hangzhou downtown railway station.

Thanks! You saved my life - otherwise I would have had no idea. But there should be some tourist information booth or at least a few English indications at Hangzhou South on how to get to the city centre...
Please note that the trip took around 50 minutes and that the South and Main stations are the two termini of the K300 line - it is impossible to make mistakes.