You can first take train from HK to Guangzhou and then transfer train from Gunagzhou railway station to Shaoxing railway station.

Use the booking service at the top of this webpage for flights. They can book you a flight from Hong Kong or from Shenzhen on the mainland side. The quickest is probably just to stay in the HK airport and fly into Hangzhou. The cheapest is probably to go to the Shenzhen airport and fly from there to Hangzhou. Most people seem to do it the latter way to save money.