From Shanghai to Hangzhou: There are frequent hing-speed trains departing from Shanghai Railway Station or Shanghai Hongqiao Railway Station to Hangzhou everyday. The journey only takes about one hour. The Shanghai Train Tickets(https://www.travelchinaguide.com/china-trains/shanghai-schedule.htm) has more details on train schedule and ticket fare.
From Shanghai to Zhouzhuang: there is no train running between them, but many tourism buses in operation. Or, you could take a train from Shanghai to Suzhou, and then transfer to Zhouzhuang by bus at Suzhou Railway Station.

Alternatively, suggested that you participate in a Shanghai Tour(https://www.travelchinaguide.com/package/shanghai.htm), covering Shanghai, Hangzhou, Suzhou and Zhouzhuang. All of these cities are included in a reguarlar Shanghai side trip. You may ask this website, Travel China Guide(https://www.travelchinaguide.com/), to arrange a tour.