How does nuclear energy change into electricity?
There are many different designs of nuclear-powered electric generation plants, but in most of them the energy released in the nuclear reactor is absorbed by high-pressure water, which is used to make steam in a secondary loop. The steam is them used to turn a turbine to generate electricity in the conventional (non-nuclear) way.
Therefore, the part of the process that actually generates the electricity is practically the same for wind-powered, coal-fired and hydroelectric generating plants. The nuclear power simply supplies the heat to boil water to turn the turbine.