how do electric dynamos create electricity simply from a few magnets and copper wiring?
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There are three things involved, movement, flow of electricity and magnetic field and they are described by what is called a Lorentz force
If you move a wire through magnetic field, you will be able to measure potential difference on its ends. What happens is (very oversimplified) as you move the electrons in wire at right angle to the magnetic field. The electron will begin to move along the wire. Thus making more of them on one end and less on another. This difference means voltage, or as you put it electricity.
And in reverse, if you push electricity through magnetic field (run electricity at right angle to the direction of magnetic field) the wire it is running through will be pushed away.
Electric motor uses the second effect, dynamo uses the first.
Dynamo rotates magnets in the middle of the coils of wire, since you now have wire moving in the magnetic field (even though it is the magnets moving), you will get voltage on the ends of the wire.
If we were to be more accurate we would be talking about force on point charges (electrons) moving in electric and magnetic fields.
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