One of the easiest ways to think about electric power generation, is to think about it as the opposite of electric power use -- kind of like a motor running backwards. Motors convert electricity into power and motion. Generators convert motion and power into electricity.
A typical generator has a large electromagnet spinning inside a stationary coil of wire. As the magnetic field produced by the ends of the magnet moves across the turns of wire in the stationary coil, an electric current is set up in the wire. Increasing the number of turns of wire in a ring or doughnut configuration increases the additive current in the wires.
Today's electricity is generated in two types of alternating current: single phase and three phase.