Here is an image of my circuit.
Here is an gif of my circuit working and alternating LEDs like a traffic light.
Here I went with 300 ohms for each LED since I knew the Arduino provided
5 volts and the circuits were in series. The LEDs are recommended to be
powered around 20 mA, so 5/.02 = 250 ohms and 330 ohms was the closest we had. I
did not want to go lower than 250 ohms, as I did not want to possibly
short my LEDs.
Here is my code with comments explaining how it works.