Pickup, some theory

So, you got the magnets and the wire. Now what?

First some theory.
To get the vibration from the (metallic) string through to your speakers it needs to be converted from vibration to an electric signal which goes into the amplifier (in between you can put your distortion, reverb or other effects).
When you bow or pluck the string it vibrates above the magnet in the pickup, generating an electric current in the electric coil around the magnet

Windings gives you resistance, the more windings the more resistance. A low number of windings gives a low output and a very clean and clear, uncoloured sound. Low resistance pickups are almost always boosted by a pre-amp. Hence the name active pickup.
A high number of windings gives a higher output, but too many windings and you loose high tones.

When using a single coil pickup you will experience the nasty effect of interference. The pickup also acts as a sort of antenna. It picks up interference from electrical things around you. What you will hear is a hum from the mains. Especially cathode ray monitors are nasty. It is a 60 hz hum in the States and a 50 hz hum in the rest of the world (as far as i know).
One way to try to get around that is to insulate the pickup with metal. In my opinion it will not completely work. If you insulate the top of the pickup, i.e. cover the magnets, the pickup will hardly pick up the vibrations from the string.
The other way is to make a humbucker. Make two pickups with reverse magnetic polarity and reverse wind them, some say that just the reverse magnetic polarity will do. That way, the hum is cancelled out. This is what i built (after i found out about the hum.....) These two pickups need to be as closely matched in resistance as possible otherwise it will not work. 

So now to building the thing > building a pickup