A Raspberry Pi controls the extremely simple electronics. Five outputs from the Pi go into a L293D dual H-bridge chip, which controls the motors. Four otuputs are for the motors, while the fifth goes into the enable pins of the chip to enable the motors. This output can be controlled with PWM to vary the speed of both motors. If you attempt to replicate the L293D setup, I recommend Adafruit's great tutorial on using the chip.
I have written some custom Python code to do some basic stuff with the soon-to-be laser cutter, but I will need to do more complex programming to get any good results. These DC motors are more complicated than stepper motors when it comes to successfully positioning the axes, so this code will have to be creative!