How can I get transportation from shanghai to Hangzhou airport?

There is no direct public transport between them. So, departing from Shanghai, you could catch a train to Hangzhou Railway Station firstly (about 25RMB). At the square of the railway station, you could take the airport shuttle bus to Hangzhou Airport with a fare of 20RMB. No need to book train ticket online~
Search the train infor at https://www.travelchinaguide.com/china-trains/