Pickups
Pickups are needed in a guitar because the the natural sound produced by an electric guitar or bass is too low to be of any practical use. A pickup consists of magnets which have copper wire wound around them. The strings of a guitar are placed over the pickups and as they vibrate they disrupt the magnetic field created by the magnets and the copper wire. This induces a current in the wire which is proportional to the vibration of the strings and it is this which enables us to amplify the sound.
Single Coil Pickups
Single coil pickups produce a bright clear sound. They consist of four to six magnets wound with 7,000 to 10,000 windings of copper wire. These pickups are very popular because of the bright sound they produce. The disadvantage with these pickups is that they are prone to electrical interference. They can begin to hum if they are near a light bulb, electrical socket etc.
Humbucker Pickups
A humbucker pickup, unlike the single coil pickup, is unaffected by interference. A humbucker consists of two identical coils wired out of phase with each having a different pole of the magnet facing the strings. A humbucker pickup produces a darker, bassier sound than a single coil pickup.
There are many different types of pickups available and below is a list of just a few:
Single coil format humbuckers
Single coil format humbuckers have their coils positioned so close together that both coils fit into a single coil spacing.
Split Pickups
Split pickups can be placed in a line but if needs be they can overlap so that each coil is responsible for one half of the string sets sound. An example of this can be seen on a precision style bass.
Active Pickups
Active pickups require their own source of power. This usually comes in the form of a nine volt battery stored somewhere in the guitar. The pickups have their own pre-amp circuit integrated into the pickup casing. These pickups give an extremely high quality signal-to-noise ratio.
the best way to choose the right pickups I have found is to pick an instrument I love the sound of and go for similar style pickups. That way you should not be disappointed with the outcome.