Hangzhou has a well-developed bus system - here's a quick and dirty guide to getting around.
The website:
http://www.hzbus.cn/Assuming you know where you wanna go, and you know where you are, click on the second radio button. I've entered in one of Hangzhou's train stations as the location, and the West Lake district as destination.
Step 2 - type or paste where you are in the left box, and your destination on the right. Hit the ask button.
A box will popup on your left. The drop down menu will ask if you prefer buses with a day or evening schedule. The second option is how far you are willing to transfer. The third option asks whether you value quicker transit times or shorter walking distances between stops.
Ideally you get something like this - a veritable cornucopia of options.
As for paying for the buses, there is a transit card, but it works as a monthly fee. Otherwise the local bus will cost between 1 and 2.5 RMB, with the mode at 2 RMB.