The summer palace can easily be reached by metro, but it takes a while to get there as it is quite a bit away from the centre. Entering from the nearest gate I first found an old street along both sides of a frozen river. The scenery is lovely. The houses are nowadays used for small shops or restaurants.
Further on you get to climb up a hill with a temple/palace on it. Many pagodas, doorways, and passageways on or through rocks make the climb very enjoyable. Once at the top, one can slowly descend again on the other side, which sports even bigger and more impressive temple structures.
Exiting the temple you reach the lake. Going left takes you to the empress dowager Cixi’s marble boat and even later on to some pretty gardens. Walking right will lead to a few more temples as well as a different gate.
Sadly, I got to the summer palace relatively late and was thus unable to explore it in its entirety, but I think I covered most of it.