The stepper motor is up and running!
For our first test we tried using the steppe motor driver from the Arduino kit, however it wasn't compatible with our stepper motor. Very sad.
We then built our own using the L293D chip, which utilizes two H-bridges, as driver from the Arduino kit. The H-bridge can be used make the steppe motor rotate clockwise and counter clockwise, depending on how the coils in the stepper motor is energized. After a while of use, the driver got very warm! So warm that you'd burn yourself and possibly wear materials around it. The reason the chip got warm is because of the voltage drop inside the chip.
Because of the relatively high currents the voltage drop produces a lot of heat, resulting in the chip getting hot. This could be solved by using a heat sink, however we chose to bring the current down using four 10 Ohm resistors.
This results in the stepper motor is operating at lower RPM but avoid overheating components. Another driver is in the mail, though.