Once you get past the reactor itself, there's very little difference between a nuclear power plant and a coal-fired or oil-fired power plant, except for the source of the heat to create steam. But as that source can emit harmful levels of radiation, extra precautions are required.
The nuclear power plant in Brokdorf, Germany.
Concrete liners encase the reactor's pressure vessels as radiation shields. Those liners are encased within much larger steel containment vessels. These vessels contain the reactor cores, as well as the equipment plant workers use to refuel and maintain the reactors. The steel containment vessels serve as a barrier to prevent leakage of any radioactive gases or fluids from the plant. An outer concrete building serves as the final layer, protecting the steel containment vessel. This concrete structure is designed to be strong enough to survive the kind of massive damage that might result from earthquakes or a crashing jet airliner. Those secondary containment structures are necessary to prevent the escape of radiation/radioactive steam in the event of an accident. The absence of secondary containment structures in Russian nuclear power plants allowed radioactive material to escape in Chernobyl. Workers in the control room at the nuclear power plant can monitor the nuclear reactor and take action if something goes wrong. Nuclear facilities also typically feature security perimeters and added personnel to help protect sensitive materials.