Begin by separating three eggs. It is easiest to separate cold eggs, but keep in mind that the egg whites should be at room temperature for this recipe. Make sure that there are no traces of yolks in the egg whites. (You can discard the yolks or save them for another use). While the egg whites are warming to room temperature, prepare the mixer bowl you will use by washing it and drying it—egg whites perform best when there is no trace of oil or other residues on the mixing bowl.
In the clean, dry bowl of a stand mixer, place the egg whites, powdered sugar, and cream of tartar. Fit the mixer with the whisk attachment, and beat all of the ingredients together on low speed until combined.
Stop the mixer and scrape down the sides of the bowl to get any unincorporated powdered sugar. A hand mixer can be used for this recipe, but it will likely take much longer to get the icing to the right consistency.
After scraping down the sides of the bowl, restart the mixer and beat the mixture on medium speed until very thick, shiny, stiff and white. This should take about 7-10 minutes, possibly much longer with a hand mixer.
Check the texture to ensure that it is suitable for your needs. If you require a stiffer icing, add a little more powdered sugar at this point.
If you want to dye your icing just one color, you can add a few drops of food coloring into the bowl and mix it for a few seconds until the coloring is evenly distributed. However, if you want to make several different colors, divide the icing into several different bowls and stir in the food coloring by hand.
Royal icing dries to a very hard consistency, and it will begin setting as soon as it is made. To prevent the icing from getting hard before you use it, thoroughly wet a paper towel and place it over the top of the icing in the bowl. It is very important to keep the icing covered! Likewise, if you are using a pastry bag and piping tips with the icing, twist the back end of the bag tightly, and wrap a wet paper towel around the tip when not in use so the icing will not dry in the tip.
Depending on the temperature, humidity, and amount of icing used, royal icing should harden within 15-60 minutes of application. Do not refrigerate products with hardened royal icing, as the icing can become soft and sticky.