Most toys/gadgets/walkmans/tape players/electronic object that needs something to move will have a motor of some kind inside it. These can be easily turned into pickups thusly:
The inside of the motor will look a bit like this, with the magnets around the edge and the coils around an axle in the middle:
Drill a small hole inbetween the coils just about big enough to not destroy the magnets like what I did on my first attempt...
Do the same on the back so that the string can travel all the way through...
Wire up the + and - terminals of the motor to a socket...
Hey Presto!
The nitty gritty of why this works is pretty simple: electric pickups on guitars are just magnets and coiled wire, the vibrations of the strings create a fluctuation in the magnetic field which creates a very small alternating current in the wire. This is then sent off to an amplifier which comes out as noise. It's all called Faraday's law of Induction which is about one of the only things I remember from physics lessons. Electric motors work using the same Law of induction, so they're built from magnets and coils just like a pickup, the only difference is how they're utilised in everyday use, innit.