I would like to take the fast train from Shanghai to Hangzhou.

Michel, you can walk from the hotel to SH Railway Station to take subway line 3 to Zhongshan Park, where transfer to line 2 to Hongqiao Railway Station. Leave through exit E and you can easily walk to the train station. Many high speed trains to Hangzhou are scheduled there. You can get a ticket on the spot and catch the train to Hangzhou in an hour.