From Guangzhou, there are three trains departing to Zhuji everyday, the fastest of which takes about 16.5 hours. The Guangzhou Trains(https://www.travelchinaguide.com/china-trains/guangzhou-schedule.htm) has detailed schedule and ticket fare.

For saving time, you could take a flight from Guangzhou to Hangzhou Xiaoshan Airport(https://www.travelchinaguide.com/cityguides/zhejiang/hangzhou/airport.htm) and then transfer to Zhuji in one hour by train or 2 hours by bus. The Guangzhou flights(https://www.travelchinaguide.com/china-flights/guangzhou.htm) only take you 2 hours to arrive in Hangzhou.