Sift the powdered sugar into a medium-sized mixing bowl. (This will make the consistency of the icing smoother.)
Add the water, and corn syrup, extract and 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 and add 2-3 drops of food coloring to each one and stir well to get 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.
Video
Notes
Make the icing thick to start and use the thicker icing to pipe the outer edges of the cookies. Then add another drop or two of water to make the icing slightly thinner to use to flood the inside of the cookie with icing.
Add a drop or two of water to thin out the icing or a few more tbsp of powdered sugar to thicken it if you get it 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 a least 2 bags of each color so they aren't fighting over the same color. Also, be sure to cut a very small hole in the bag so they don't squeeze too much out at once.