Shanghai is the biggest city in China with many direct/indirect flights from all over the world. Once you are in Shanghai, it is only 2 hours' drive on expressway to reach Hangzhou. Shuttle buses are available every 90 minutes from Shanghai Pudong International Airport and Shanghai Hongqiao International Airport to Hangzhou's city center (Wu Lin Men), costing RMB85.

There are also shuttle buses every 90 minutes from Shanghai Pudong International Airport to Hangzhou Dragon Sports Center, costing RMB100. So if you fly to Shanghai, it is very easy for you to reach Hangzhou.

Here's the schedule of the shuttle bus:
Pudong Airport-->Dragon Sports Center: 10:30, 12:00, 13:30, 15:30, 17:30, 19:00
Pudong Airport-->Wu Lin Men: 8:40, 10:10, 11:40, 13:10, 14:40, 16:10, 17:50
If you are already in Shanghai, you can take bus or train. Buses depart every hour from Shanghai Long-Distance Bus Station to Hangzhou Long-Distance Bus Station. Express train takes 2 hours and normal train takes 3 hours. Here's the schedule of some of the trains:

Given the capital status of Beijing, flight connection to Beijing is excellent. Once you are in Beijing, you can connect a flight to Hangzhou, which takes about 2 hours.

You can also consider taking the train from Beijing to Hangzhou. The fastest train between the two cities takes about 13 hours, departing at 18:53, arriving at 8:23 the following morning. Here's the train schedule for your reference: