A very helpful page for completing this assignment was Dan Chen's guide to designing the Hello World board with LEDs. Some helpful tips that I learned from the recitation were to not pass a current of more than 20 mA through an LED (check the data sheet if not sure about the exact value), and that LEDs have forward voltages.
The circuit designer that I used to modify the Hello World board was Eagle. There are many good tutorials for Eagle on the SparkFun website. In addition to downloading Eagle, I also had to download the fab library which contained relevant components and move it to the libraries directory (Options->Directories).
Before exporting the board to png files which could then be milled using the fab module, I had to do several things. First, I had to run the DRC command, which automatically does the design rule check.