"I don't have confectioners' sugar—can I just use the same amount of regular granulated sugar?"
Confectioners' or powdered sugar, is finely ground sugar with a little cornstarch added; it is lighter and fluffier—more powdery—than granulated sugar. Because of its finer texture, confectioners' sugar is ideally suited for use in icings, which would be slightly grainy when made with granulated sugar.
Confectioners' sugar weighs less per cup; substitute 1 3/4 cup for every cup of granulated sugar called for.
For more information on using different types of sugar, see 7 Ways with Sugar.