The easiest way to incorporate espresso powder is to mix it with the dry ingredients included in your chocolate cake recipe. Usually this means sugar, flour, cocoa powder, baking powder, baking soda and salt. It doesn’t change the ratio of dry to liquid ingredients (much), so you can usually use it in almost any chocolate cake recipe without needing to change anything else. Be careful not to overuse it. Otherwise, your dessert may end up tasting like mocha instead of real chocolate.
However, even if you have a recipe with freshly brewed coffee in the ingredient list (à la Garten), you can substitute espresso powder. Simply use as much hot water as you need coffee and stir dry espresso until completely dissolved. Even if your recipe doesn’t include coffee (or any other caffeine-based ingredient), stirring coffee in hot water can enhance the chocolate flavor even more than using the raw powder. In this case, be sure to adjust other liquid ingredients in the recipe (such as milk) to avoid an overly moist dessert. It may take a little practice, but the result is a delicious, rich chocolate cake.