Shijiazhuang has a metro system with several lines covering the main urban areas. Buses are extensive but hard to navigate without some Chinese. Taxis are plentiful and relatively inexpensive by Chinese standards.
For the outlying sites — the Zhaozhou Bridge, Longxing Temple, Bailin Monastery, Mount Cangyan — the easiest option is to hire a taxi for the day or use one of the dedicated day-trip services that operate from the main hotels. These typically charge a fixed price for a circuit of two or three sites and save considerable time over trying to use public buses to reach rural Hebei.