How does a nuclear power plant work?

Atomic nuclei are composed of neutrons and protons. Some heavy nuclei, such as uranium-235 (which contains 235 protons and neutrons), undergo fission when they absorb an additional neutron and become uranium-236.
When an atom fissions, or splits, it releases heat energy and 2-4 additional neutrons. If there is enough uranium-235 fuel, it is likely that the newly released neutrons will be absorbed in the fuel and cause more fissions. The heat energy produced from the fissions is the source of nuclear energy (so that the power produced is directly proportional to the fission rate).

Fission only occurs with a few nuclei, so the key to controlling the chain reaction is to change the average fraction of the 2-4 neutrons produced per fission which are absorbed in the uranium fuel. This can be done by inserting/removing a non-fissile control rod as needed. In the diagram above, the rods are visible in the pink reactor vessel.

In a Pressurized Water Reactor (PWR), the uranium is located in the core (red) . Heat generated from the fissioning of uranium is transferred to circulating water in the primary loop (pink). The primary loop is kept at high pressure, so that even though the water temperature is greater than 212 degrees F , it does not boil.

The primary loop passes through a steam generator, where it warms the secondary loop. The secondary loop water changes to steam in the steam generator. The generated steam is then used to turn a turbine, which is connected to a generator. The turning generator then produces electricity.

After passing over the turbine, the steam is cooled by a third loop from a cooling tower or pond and sent back to the steam generator to repeat the cycle.

Nuclear energy is clean because of the large amount of energy released per fission. In fact, since nuclear cores are only replaced about once every five years (1/3 replaced every 18 months), very little waste is generated.

Your total share of the yearly nuclear fuel waste, if all electricity in the U.S. were produced by nuclear power, would be about the size of a thimble.