Here's an image I found in a patent for an r/w head:

It's from US Patent 4,251,842 - Magnetic Recording and Reproducing Device
That gives you the basic idea of what's going on, (ignoring 7 and 5 for now) there's a coil for inducing a magnetic field and a bit of metal for directing that field across a gap which will then organize the magnetic material on whatever media it's traversing. And it works both ways, the magnetic media can induce an alternating current in the metal which gets translated to the coil and back out to where we can hear it.
______________________________________________________
Now, if you look closely at your own floppy drive, you should be able to locate the head.
1. Here's a random drive I just happen to have lying around (I have a lot of them for some reason :)

2. Each drive and drive manufacturer was different, so the covers and cases are all secured differently. Here's that Mitsumi with the cover removed:

3. The two head arms are designed to squeeze the doublesided 3.5 inch diskette and sandwich it between the read/write heads. Two separate ribbon cables come out of the arms, one for each head.

4. Pardon the blurriness here, but having removed one of the ribbon cables you can see that there are more than two connections per head, in fact there are five different contact points.

______________________________________________________
So why five contact points? This is so that the heads could do something called "tunnel erase", basically trimming the edges of a data write in order to keep the tracks from bleeding into each other on the disk and corrupting the data.
With a graphic I found on page 647 of Scott Mueller's "Upgrading and Repairing PCs"
you can picture the head looking like something like this:

Personally, I'm pretty sure that this bleeding across tracks is partly what's responsible for the cool sound that happens when you use the system to write audio, so needless to say we don't really have to worry about it too much. However, to get more familiar with the head, let's take a look at those 5 connections.
Here's a cool graphic I found in another patent:

from European Patent Application #82104726.3
Notice how one of the connections doesn't seem to be going to anything? That's actually connected to the shield, which can come in handy later. In this diagram it's the middle connector, that won't necessarily be the case in your floppy drive.
In order to figure out what's what, you should take out your multimeter and start probing the leads. It can be a pain to probe the leads on the tiny flex cable, so you can try a trick that I figured out at some point which was to tape the cable down. That way you're not too likely to rip it and it will help a ton when you want to probe it or solder it later.
This is a photo of one of the half height TEAC drives that I did my project with, those things were tiny!

When you take out your multimeter to probe the connections, you will find one that has a very large resistance from the others (that's the shield line) but you may be surprised to find that all of the other lines are virtually shorted to each other. In reality they have a very small resistance, but they are all connected.
Trying to figure out what was going on with the head made a lot more sense when I discovered this diagram in a Commodore 64 manual:

Back when it was worth trying to fix floppy drives they provided this diagram and gave the proper resistance for each coil and how they should look when you were probing each section. I went ahead and labeled these since you'll have to figure out what part is which on your own.
A couple of useful observations: The resistance between A and C should be the same as the resistance between A->B and B->C added together. or:
A->C = (A->B) + (B->C)
also:
A->D = (A->B) + (B->D)
and:
C->D = (C->B) + (B->D)
I made a little chart for each head I was working on and then labeled each connection so that I would know what it should look like. It doesn't have to be pretty, this is how mine looked:

Positioning a probe on line 1 (as drawn on the page), I measured and recorded the resistance between 1 and each of the other non-shield lines. Then I did the same with 2 and 3. I drew out the diagram found in the commodore manual and did the algebra by intuition. The two smallest figures conveniently add up to the resistance between 1 and 2, which leaves only 4 standing on its own. If memory serves each floppy drive I discovered followed this pinout, but it's fun to draw the little diagrams and it makes you feel good.
Once you've got it all figured out, you can either pick two and solder them up, or solder up all 5 and pick later. Don't forget to wire up the shield as well. If you have trouble soldering regular wires to the small connectors, you can try magnet wire. That worked really well for me:

I taped them all down and then soldered them one by one.
Okay I have to run for now, but more to come soon. Let me know if anyone has any questions!