We don't have subway from the airport to the city at the moment. Work is underway and its schedule opening is 2021
The 2 options to get in from the airport are taxi and shuttle buses
Taxi: taxis boarding area is outside of gate 4 (int'l) or gate 10 (domestic). Fare to the city is around ¥110-¥140 RMB, or $16-$20 USD. The journey takes 40-50 minutes
Shuttle buses: much cheaper than taxi and you can find them outside of gate 14 at the domestic arrival area. There are over 50 shuttle buses from the airport but only 2 of them transport you to the city center of Hangzhou.
Bus 1: Wulinmen Line (武林门专线)
Runs everyday between 7:30am and the last flight of the day. Every 15 minutes before 10pm and every 30 minutes after 10pm
Fare: ¥20 RMB per passenger, equivalent to about $3 USD