Devil's food cake turned out dry and dense

For this recipe, the most likely issues are:

• overbaking and wrong oven temperature
  Simply put, removing too much humidity during the baking process. Wrong oven temperature can aggravate this problem, especially if it is too low (to hot = burned edges and wet center).

• over-mixing
  This recipe is very sensitive to overmixing, which means forming gluten strands that make your cake dense. Alton Brown specifies the mixing time in seconds for a reason. As a beginner, you could use a whisk instead of a mixer and stir just until the "just combined" or "no more lumps" stage, not more.
  Technically it uses the same technique as muffins, not the beat eggs / butter / sugar until fluffy technique known from cupcakes

• waiting before baking
  This recipe gets its "lift" almost exclusively from baking powder. It is activated the moment it gets wet and then even more when heated. So if you don't bake the batter right away, it may "fizz out" somewhat, leaving you with a dense cake. This will take longer to fully bake and again be dry.

• wrong measurements
  The recipe states "ounces", which is a weight unit. I other words, you need a scale to measure your flour and cocoa. While a (US) fluid ounce is two tablespoons or 30 ml, an ounce is 28.3 grams. So for water, you can roughly exchange one for the other, but never, ever for other materials, especially light and dry stuff like flour.
  (Yes, I have seen this happen.)

From your comments, overbaking might be the main problem here, possibly combined with overmixing.