How do humbuckers work?
Humbuckers are basically two single coils arranged side-by-side (fig. 1), each with six magnetic poles or slugs (one for each string). They are wired in a way that cancels the unwanted frequency and keeps as many of the good frequencies as possible.
Most modern Stratocaster guitars (fig. 2) have a humbucking option built in. The middle pickup is reverse-wound/reverse-polarity to the neck and bridge, so that when they are used in combination they will cancel any hum. This only works because the two coils are so far apart and the harmonic frequencies are so different, the only quality that is the same about them is the hum, so when the two coils are opposite, they cancel the hum.
fig. 2 the middle and bridge or middle and neck pickups are hum-canceling together
Humbuckers function a little differently than this. Since the coils are so close together (as close as they can possibly be without being on top of each other), they are sensing very similar sounds and they need to be out of phase to cancel the hum. Humbuckers consist of two coils (both wound counter-clockwise) with opposite magnetic poles facing up, usually wired in series.
Some people don't like how humbuckers aren't as clear or bright as single coils, but what a lot of people don't realize is that there are many different ways of building humbuckers to change the tone. The original Seth Lover PAF humbucker (which is the baseline against which all other humbuckers are judged) consists of 5000 uniform winds per coil (not scatterwound), bar magnets mounted underneath, adjustable poles on one side, slugs on the other, topped off with a nickel-silver cover. All of this makes for a pretty dark sounding pickup. Which might sound great in certain guitars, but some guitars beg for bright, twangy tones. You could use scatterwound coils (for a brighter, clearer sound) and solid Alnico polepieces much like a Strat pickup. This is the formula I used for my Apex Humbuckers.
fig. 3 my Apex Humbucker
You could also have an underwound humbucker (say with 4000 winds per coil) for a brighter tone, and you could wire these coils in parallel (instead of in series) for pickup with a clear tone and absolutely no hum.
So there are lots of different options when it comes to getting different tones out of humbuckers, they don't always have to be dark sounding. Most modern humbuckers come with 4 conductor leads so you can split the coils, and you can look up a wiring diagram here to experiment a bit. Knowing your color codes of your pickup wires will be very helpful too, here is a link to color codes of a number of popular humbucker manufacturers.