How would I go from Peking University to Beijing International School using public transportation?

There is no direct public bus or subway. You need to transfer. Take subway line 4 at East Gate of Peking University, and get off at Haidian Huangzhuang Station. Then transfer to subway line 10 to Sanyuanqiao Station, Exit C3, and take public bus no. 942 to the international school directly. After arriving, walk to the destination directly.