I've just taken apart a CD drive.
There's a small stepper motor which was used to move the laser. The connection to this motor is a four-strand thin ribbon.
How do I connect that cable to a circuit? Preferably onto a breadboard.
What's the female connector thingy called for it?
You could carefully cut between each connection and then solder each one onto a wire.
Or you could get a plug/breakout board for that sized connection.
Mowcius
You could carefully cut between each connection and then solder each one onto a wire.
If you are unable to solder the connection (for instance, if the ribbon's substrate is plastic - typically polyester - and can't take the soldering heat), there do exist silver and other conductive "glues" that you can use to glue a wire to each junction.
There's a small stepper motor which was used to move the laser.
I think you will find it is not a stepping motor but just a DC motor.
How come grumpy mike?
It controls the position of the laser, which needs to be very precise and it isn't geared. It has four wires coming from it.
Here's a picture of the rig: link.
Motor is bottom right. You can see the spiral shaft coming out of it, the laser rig runs up and down.
There was another motor in there for opening the tray which is just a motor, and the motor for spinning the disc which I binned because it looks a little complicated (about a dozen wires to it).
edit: link fixed
Well at the moment I am collecting scrap CD drives from work for a project that is going to use 24 of them (only got 14 so far). All the ones I have taken apart so far have a DC motor in this position and look exactly like your photograph. On a CD drive the positional feedback is taken from the disc itself so there is no need for a stepping motor here. I must admit I was expecting a stepping motor in this position, but I am finding DC motors. The ones I have pulled apart only have two. You say it has four wires but all mine only have two.
That's a shame, but I should still be able to make use of it anyway.
I'll throw some power at it and see what happens 
I wonder if anyone's ever tried to make a minature CNC machine with one of those?
I gave it 5v, it moved a tiny bit. Does this mean it's likely to be a stepper motor?
maybe...
or it moved then broke ;D
I wonder if its possible that it could be a brushless DC (3-phase) motor?
Mowcius, it did it more than once so it's not broken. I hope! It didn't trip the power supply either.
Now, how do I go about getting it to work?
Now, how do I go about getting it to work?
Get a H-bridge driver circuit for each coil and pulse them.
Something like:-
http://www.thebox.myzen.co.uk/Workshop/Motors_4.html
I'm pretty sure I have one of these in my bits box: http://www.earthshineelectronics.com/13-motor-driver-ic-s
Guess it's time I learnt how it works!
It IS a stepper motor 
Right, one 'people on this website at the moment' counter coming right up.
