Sift the powdered sugar into a medium-sized mixing bowl. (This will make the consistency of the icing smoother.)
Add the water, corn syrup, and extract, then stir with a fork until it forms a smooth paste.
Add a few extra drops of water until you get the right consistency. It should be a glue-like consistency for piping.
Divide the white icing into small separate bowls, add 2-3 drops of food coloring to each, and stir well to obtain different colors.
Put the icing into a piping bag (or Ziploc bag with a tiny hole cut in the corner) and pipe it onto your favorite cut-out cookies.
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Notes
Make the icing thick initially, and use it to pipe the outer edges of the cookies. Then add another drop or two of water to make the icing slightly thinner for flooding the inside of the cookie.
Add a drop or two of water to thin the icing, or a few more tbsp of powdered sugar to thicken it if it is too thin.
Add sprinkles to the cookies immediately after piping on the royal icing so that they stick better.
When decorating cookies with kids - I like to make up a double batch of royal icing and fill up little snack-sized ziplock bags with the icing. I make at least 2 bags of each color so they aren't fighting over the same color. Also, be sure to cut a tiny hole in the bag so they don't squeeze too much out at once.