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The main concept is in having a magnet moving close to a wire.
The wire is formed in a loop so current can flow full circle.
The current direction depends on the pole of the magnet and the relative motion.
The wire can be wound multiple times, and additional magnets can be arranged, so as to create multiple interactions, joining together so that they reinforce the current.
The closer the interactions...
or the more of them there are...
or the stronger the magnet...
or the faster the motion...
the more power you can generate.
That's the core concept.
To generate power at low cost, it usually requires that you go to more effort in some way, shape or form. Such as more labor in turning the generator, etc.
It is possible to light up an led by waving a magnet near a coil of wire which is hooked up to the led.
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