I'm not sure what your level is. If you don't know how to turn something on and off with an arduino and a transistor, start there. A transistor array is just a package of many transistors together (7 in this case but I only use 4) and they are used to turn on and off the four coil pairs. The chip on the side is a ULN2003 transistor array. I connected four outputs from the digispark (0,1,2,4 not 5 because its high is only 3V and not 3 because I didn't understand the note about its internal pullup or down resistor) to four inputs on the transistor array. Opposite coils are connected to each other. So the four pairs are connected to the outputs of the transistor array- basically when you set, say, pin 0 HIGH, the corresponding coil pair is turned on. Cycling through each pair spins the motor. That's really all the code is. To make it go in reverse you reverse the order of turning on the coils. If you search ULN2003 and stepper motor you'll see lots of schematics. Cheap Chinese 5V stepper motors on Ebay come with a little board with this chip. Does that help?
