Do you want to read/write data? That would be a huge challenge.
If all you want to do is spin the motor and move the heads in and out, it's just a matter of twiddling a few digital lines. It's been so long since I worked with low-level floppy controller software I've forgotten the details, but I'm sure they're on the web.
Upping this post, since I'm planning to make an Arduino-based floppy controller :-D. I'll get started asap. I'd love to see the photos from Hyperjer's post though but the links are broken...
If you do some searching for "floppy the robot", you'll find info about how to interface with the port on the floppy to control the motors. The project details using a floppy drive as a crude robot chassis (interfaced to the parallel port, or maybe a PIC or Basic Stamp - I forget).
Interfacing with the drive itself to read/write data is a whole 'nother thing entirely - I'm not even sure if the interface is 16 bit or 8 bit, off the top of my head - it should be possible to do - but whether there is enough code/data/ram space on the Arduino to do it or be useful is different issue...