In Shanghai, there are two airports. I think you should arrive Shanghai Pudong Airport. You could come to Hangzhou by coach (from Pudong to Hangzhou), takes RMB 100.00. On the way will be 3 hours.
Or you by taxi or Pudong Bus to Shanghai South Railway Station. (By taxi will be RMB 200.00, by Bus will be RMB 20-30.00/person). At the Shanghai South Raiway Station, will be comfortable train directly to Hangzhou, ticket will be about 54.00-64.00/person for different class by the High speed train.