After visiting badaling great wall, how can I go to summer palace? Are there taxis or ...?

You can choose to take a taxi to get there directly, but it is around 65km between, so it may charge a little high. By public transportation, I suggest you take bus no. 877, 880 or 919 back to Deshengmen in Beijing. Then walk to Jishuitan metro station to take subway line 2 to Xizhimen and then transfer to line 4 to Beigongmen. Then you can easily find Summer Palace.