To create the dot density map I displayed the shapefile I was working with using the Dot Density option hidden in the file's Properties under the Symbology tab. It took a little while to decide which dot size and dot value to use because the clarity of the dots changed as I zoomed in and out of the map and it took me a while to realize this. Eventually I settled with a dot size of 2 and a dot value of 10,000. I was able to adjust the placement of the dots (excluding certain areas like large water features) by using the Properties option within the Dot Density window. As a note to anyone who wants to use this feature, it does not work well if you turn these options on and off several time so save your map often.
Aside from ArcMap being a little finicky the map was not difficult to make. The difficult part was finding a color scheme that worked well with all of the required map information. I had to include multiple water features that needed to be displayed in blues and greens. This major use of blues and greens washed out most of the other color options for the dots and since they are the most important feature, they need to stand out. I tried several bright colors and dark colors but the only dot color that stood out well against all of the water features was a bright pink. I even made most of the other features on the map partially transparent but pink was the only color that seemed to work.