Most thermal power plants use fuel to heat up water from a reservoir, which generates steam(usually at a high pressure). The highly pressurised steam then travels through pipes to rotate the fan-like blades of a turbine (see Rankine cycle for more info). As the turbine begins to spin, it causes giant wire coils inside the generator to turn. This creates relative (continuous) motion between a coil of wire and a magnet, which pushes electrons and starts the flow of electricity.
Nuclear power plants use fission processes to generate electricity. In these plants, uranium nuclei are split which creates the thermal energy needed to create steam. It then works just like fossil fuel power plants where the steam spins a turbine, generating electricity. The power plants require the use of nuclear reactors to carry out these fission processes. Some types of reactors include pressurized water reactors, CANDU reactors, RBMK reactors, and boiling water reactors.