How to get from Shanghai to Hangzhou by train/bus?

If by train, you can take a high speed train at Shanghai Hongqiao Railway Station. Every day, there are lots of trains that can take you HZ Railway Station directly.
If by bus, lots of long-distance buses are bounded for HZ in Shanghai General Bus Station and South Bus Station. You can go to take it. The ticket fare is CNY 68 per adult.

What is the average cost for a high speed train from HZ to SH?

About high-speed train, the ticket fare of the first class seat is about CNY60 and second class seat is about CNY 50. The G trains are a little expensive than the D types, but faster. You may check the real-time schedule and ticket fare on this site.