Series vs. Parallel Wiring and Switching
Different coils and pickups yield dramatically different sounds when they are combined in different ways.  The pictures below demonstrate the differences in the wiring.  Note that the coils do not have to be part of the same pickup.  In spite of these images, the coils can be individual single coils or the coils of a humbucker.

However, on a humbucker you usually will not see the wires extending directly from the pickup.  Most manufacturers wrap all the wires (aka "conductors") together so that you have one shielded length of cable with only the ends of the wires protruding.  The moral is that the pictures below are there to help you visualize the wiring, not necessarily to work directly with it.

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Series wiring
This is the standard wiring scheme for humbucking pickups.  However, in a humbucking pickup guitar such as a Les Paul, things are a little more complicated.  Within a given pickup, the coils are summed in series, but when both pickups are selected together, the output of each pickup is combined in parallel.
Parallel wiring
In the majority of single coil guitars such as Fender Strats, the coils are added together in parallel.  This gives the nice characteristic "bell"-like or "glassy" sound.  This is far less commonly found in humbuckers, but it can be achieved by switching the wiring as shown below.

Series/Parallel Switching
The illustration at the left shows how to put a series/parallel wiring switch on a push-pull pot (I don't have the pot wired in this picture; it can serve any function).  You don't have to use a push-pull pot as any DPDT (double pole-double throw) switch will work.
The bottom configuration (the way it would be if you had the push-pull pushed) is series (standard humbucking scheme).  The top (pulled) configuration is parallel.  You would probably reverse this (flip the connections upside-down) if you were performing this modification on a single coil guitar.

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