The turning of a coil in a magnetic field produces motional emfs in both sides of the coil which add. Since the component of the velocity perpendicular to the magnetic field changes sinusoidally with the rotation, the generated voltage is sinusoidal or AC. This process can be described in terms of Faraday's law when you see that the rotation of the coil continually changes the magnetic flux through the coil and therefore generates a voltage.
Below is an illustration of how an an alternating current is produced in an AC Generator.

Motional EMF

The magnetic force exerted on the charges in a moving conductor will generate a voltage (a motional emf). The generated voltage can be seen to be the work done per unit charge. This motional emf is one of many settings in which the generated emf is described by Faraday's Law.
Note that the direction of the magnetic force is shown as the right hand rule direction on a positive charge, and shows the direction of the conventional current in the loop.

Motional EMF and Faraday's Law

The motional emf expression is an application of Faraday's Law, as can be seen from:
You could refer to the below powerpoint and a short compiled notes for a more detailed view on the AC Generator and almost all electricity topics thereafter.

Electricity notes:

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Electromagnetic induction is the basic principle for the working of generators.

How does one of this generator works?

The following websites provide simulations of generator. You may want to explore theses sites to figure out how a generator works.

The following websites provide explaination of how an AC generator works. Access Code :- SMTP4S2ACgenerator

Compare and contrast AC and DC generators