First, the custom-made program that will run on your computer is capable of scanning a bitmap and sending instruction to the arduino via the USB port.
Next, the arduino will send instruction to the CNC-shield (a stepper motor driving module mostly). This step will be either manual, using a remote control, or automatic: the arduino sends instructions to the cnc shield according to what it gets from the computer.
The CNC-shield will recive instruction from the Arduino and simply drive the CNC router.
Finally, the hardware will be animated by the above devices.