How is power generated?
If a magnet is inserted into a coil of conducting wire an instantaneous current occurs in the wire which will produce a voltage which can be observed with a voltmeter; when the magnet is removed from the coil another instantaneous but opposing voltage can be observed.
This effect, whereby the relative motion of a magnet and an electric coil produce a current, is known as electromagnetic induction and was simultaneously discovered in 1831 by Michael Faraday (1791-1867, England) and Joseph Henry (1799-1878, America). Faraday developed the first dynamo (generator) in which the continuous rotation of a conducting copper plate between the poles of a magnet produced a continuous current.
Primitive electric generators were in use for various experimental purposes very soon after Faraday's 1831 discovery, but it was about 50 years before commercial generators came into use after Werner Siemens (1816-1892, Germany) perfected a generator in which part of the generator's working current is used to power the field windings, eliminating both the need for permanent magnets and one of the basic limits to generating electric power. In a generator, mechanical energy is converted into electrical energy via a magnetic field.
In a hydroelectric power plant the motion of water is used to move big fan like blades in a turbine to then turn a shaft connected to a generator. The generator has a powerful electromagnet (a rotor) which is turned inside a "'coil" of copper bars (a stator). This produces "electromotive force," or the process of exciting electrons to jump from atom to atom. When electrons flow along a wire or other conductor, jumping from atom to atom, they create an electric current, or a flow of electricity.
Generators cannot store the energy they create. Once the mechanical energy from the flow of water is converted into electricity it must be used immediately. Therefore, electric demand must be well anticipated to avoid wasting the resources used to make electricity.
More general information and diagrams can be found at the Foundation for Water and Energy Education (FWEE), the Canadian Hydropower Association or the U.S. DOE , Department of Energy Efficiency and Renewable Energy.