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...
In this demonstration I made a very basic instrument construction just to show how the pickup is used. I will talk about this in the last step. How you adapt your own version to your instrument depends entirely on your imagination!
Step 1: The Motor
Take off the plastic backing on the motor, the inside will look a bit like this, with the magnets around the edge and the coils around an axle in the middle.
Step 2: Small Holes
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...
its a good idea to glue the axle so that it doesn't spin.
Step 3: Small Solderings
Wire up the + and - terminals of the motor to a socket...
it doesn't matter which wire goes where.
Step 4: Ta Daa!
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.
The 'instrument' in the demonstration below was a simple one-stringed instrument with a tuning peg at one end and an anchor at the other (for ideas on homemade/DIY tuning pegs, check out my post on it at my blog here.
I used two small L-Brackets in order to get the wire to the right height to pass through the motor without it touching the sides.
I've included an image of the pickup in-use in an instrument I built. The axle on the motor was at a different angle that allowed 2 strings to go through it.