Besides the instructions following this introduction, I always add 1/2 tsp of cream of tartar to the egg whites mixture:

How to Make Meringue:
Make sure your egg whites are room temperature.

For safest storage always keep eggs in their carton in the refrigerator until you are ready to use them. For meringues, you'll need only egg whites and they should first be brought to room temperature so they'll reach their fullest volume. To quickly warm eggs from the refrigerator, place whole eggs in their shells in a bowl of very warm water to cover 10 minutes. Carefully drain water from bowl.

Carefully separate whites from yolks (do not allow any yolk to mix with the whites) into a clean, dry mixer bowl. Beat the whites at medium speed (as your recipe states) until mixture forms bubbles and is frothy.

Continue to beat at medium speed, gradually adding granulated sugar, 1 tablespoon at a time, until all the sugar is incorporated and the mixture holds a soft peak when beaters are lifted. Gradually increase mixer speed to medium-high and continue to beat until whites are thick and glossy and hold a stiff peak when beaters are lifted.

For baked meringue shells: Line a large cookie sheet with parchment paper (dab a dot of meringue on each corner of the sheet). Cut a piece of parchment to fit the sheet; draw circles as directed in recipe with pencil and invert parchment onto prepared sheet, pressing gently in corners to adhere. Fill a large pastry bag fitted with a 3/4- to 1-inch round tip. Pipe meringue within the circles; starting from outside of circle and filling in. With the back of a spoon gently swirl meringue to form a nest shape. Bake and cool completely as directed.

Fill baked shells with fresh berries, ice cream, sorbet or chocolate mousse.