Spoon some of the thick white icing into individual bowls and add coloring
For each color of icing, you will want a piping bag (or squeeze bottle) of thick icing and one in the same color of thinned icing.
Once you color a bowl of icing, scoop about 1/2 of it into a piping bag (fitted with a size 2 tip- or other desired size), and then thin the remaining icing in that bowl to create a thinned version of the exact same color.
To thin icing add 1 teaspoon of water at a time and stir, continue adding water by 1/2 teaspoons until desired consistency is reached.
Notes
Make sure all bowls and utensils are totally grease-free or your icing will never reach proper consistency.