Quite a bit, because ground ginger is very potent. It also does not taste very much like fresh ginger, so most people would tell you to avoid making the substitution - and certainly to think twice before going the other way and substituting ginger powder for fresh ginger.
Dried ginger works well in many savory dishes, such as soups, curries, and meats, in many fruit dishes, and is indispensable in such baked goods as gingerbread and gingersnaps, according to Sharon Tyler Herbst, author of The Food Lover's Tiptionary. Fresh ginger can be used in a much broader range of dishes.
The one reference we've found that gives a substitution hint for going from fresh ginger to powdered says to use 1/8 teaspoon of powder for every tablespoon of ginger. So that would suggest using 8 tablespoons, or a half cup, of ginger for your teaspoon of powder. Depending on the recipe, the addition of that much added food could really upset the finished dish. But we'll leave that decision up to you.