Probably the simplest drive possible is one made with nothing more than 2 flip flops:
Note the LEDs are not needed, they are only there to show the coil signals.
Here it is on a breadboard:
And here is one running:
Stepper motor driven by 7476 dual JK flip-flop from Tatzelbrumm on Vimeo.
Now, please note there are many problems with this:
But the point here isn't to build a great driver, it's to learn how the sequence of signals can be made. These issues can be overcome^ but less expensive drivers are a better choice for actual use. The problem: You never learn how they work!
Also: Digital Logic Tutorial