Preheat oven to 225 degrees F. Line a large baking sheet with parchment paper; set aside.
Using an electric mixer with the whisk attachment (or a hand mixer), beat the egg whites on medium speed until frothy, then add the cream of tartar, salt, and vanilla extract.
Increase the mixer speed to medium-high and beat to soft peaks. While continuing to beat the egg whites, gradually add the granulated sugar and beat until glossy and stiff peaks form.
Fit a pastry bag with a large star tip (I use the Ateco #827 for an open star, the Ateco #864 for a French star) and fill it with meringue.
Pipe the cookies onto the prepared baking sheet. You do not need to leave much room between the cookies, as they will not spread.
Bake the cookies for 1 hour, or until firm to the touch. Turn the oven off and prop the oven door open with a wooden spoon until the cookies are completely cool. (I usually bake them in the evening and then leave them in the propped-open oven overnight to cool and set up completely.)
Carefully remove from the parchment and store in an airtight container at room temperature, keeping them away from excess heat or moisture (it will cause them to become chewy).
Notes
Eggs: Use room temperature eggs. Egg whites from a box or carton are not recommended.
Clean bowl and utensils: Even the slightest hint of fat (egg yolk, residual oil on a bowl or beaters, etc.) can prevent the egg whites from reaching stiff peaks. Ensure that everything is completely clean and dry before beginning.
Gradually add the sugar: It's important to add the sugar only a little bit at a time (a couple of tablespoons); adding it slowly ensures that the sugar gets absorbed into the egg whites and eliminates a gritty texture, and also reduces the chances of the meringue collapsing and failing to reach stiff peaks (this can happen if a lot of sugar is added all at once).
You can't overbeat meringue: It's true! You can't ruin it by mixing too much, so once all of the sugar is added, be sure that your meringue is glossy and that you have super firm, stiff peaks when you remove the beater from the mixer. Don't be afraid to mix a little longer if it appears too soft.
Adding colors/flavors: If you want to add different flavors, you should do so when the vanilla extract is added. To make a colored meringue, add food coloring (I recommend gel food coloring to eliminate extra liquid being introduced into the meringue) once the meringue has reached stiff peaks, and beat until the color is completely incorporated.
Equipment: The easiest way to make meringue is with a stand mixer (hands-free!), but I routinely make it with my trusty hand mixer. You can also make it by hand, just use a large wire whisk and some elbow grease! It will take a little longer, but it can be done!
Weather: Meringue is notoriously sticky and difficult to whip into stiff peaks on humid days. While central heating and cooling eliminate most problems, I do notice a difference when I work with meringue or bread dough on a dry winter day vs a warm summer day, even with central air. To keep issues at bay, opt for a day with low humidity.