Build this ultra-simple AC electric generator from magnets, wire, and cardboard. (And a big nail!) Light a small lightbulb, or flash a red LED.
This demonstrates how generators work. Now if you want a more useful device, use a small DC motor as a generator, since it has much better magnetics design. All motors are generators. Figure out how to spin a motor's shaft, and you can make a small powerful generator. Or... figure out how to convert the cardboard generator into a motor!