Why you'd want additional wires is what
much of the rest of this site is about. Many hacks such as coil tapping,
series/parallel connections within a pickup and phase switching within
a humbucker (or any combination of all of those) assume you have selective
access to each coil within each pickup. If you only have two wires,
then sorry, you don't.
As you know from the Basics sections that you probably shouldn't have skipped past, humbuckers are composed of two coils, each of which has a start and finish to its windings. Where two-conductors differ is that there's a continuous connection between one coil and the next, so you're only going to have the start of one (or both, technically) and the end of everything. We're going to fix that..
There are two ways to go about this which will result in either a two- or a three-conductor pickup in the end.
I can't go into the particulars of this job because there are several ways to construct a pickup and, conversely, different ways you'd be forced to access the windings. On most open-face humbuckers, you can peel the cloth covering away from the bobbin to see this connection, but that may not be true in every pickup. One reader told me he removes the base plate. Just depends on the pickup. There's enough variety out there that you'll be exploring territory that few others have charted, myself included in any case.
Like I alluded to above, I have never performed this conversion. I include it here for the sake of completeness, but in addition to being a somewhat tedious and delicate procedure, it is also something of an unnecessary mod. If you have a two-conductor humbucker, odds it is a cheaply made one. Manufacturers looking to cut costs are the ones most inclined to include these on their instruments, and those aren't usually the best-sounding devices. I describe this mod as redundant because if you're going to take the pickup out, why put the same cheap thing back in your guitar? Why not upgrade to something more voiced to the style(s) you play? Why not go with one with a better (i.e., stronger) output than the under-wound Made In Taiwan pickup you started with?
That being said, I know a lot of folks get attached to a characteristic sound of their stock pickups and only want more options, not a different tone entirely. If so, feel free to hack away here.