Line several sheet pans with parchment paper. Alternatively, you can simply lay the parchment out on any table or other surface where the sprinkles can be left to dry overnight.
While you are mixing the colored icing and piping the sprinkles, keep a damp kitchen or paper towel over the rest of the uncolored royal icing. It dries very easily and the crusty bits will clog your piping tip.
Working with one color at a time, scoop out some of the royal icing into a small bowl, and mix in your choice of food coloring. Transfer the colored royal icing to a piping bag fitted with a small round tip. Choose the tip based on how thick or thin you want your sprinkles to be. No pastry bags? Use a zip-top bag and cut the tip off of one corner.
Pipe the royal icing out onto the parchment in long parallel lines. There is no need to be perfect! Feel free to go very quickly and don't worry about bobbles and squiggles.
Allow the royal icing to dry for several hours, preferably overnight, until very dry and crunchy. With clean hands, break the dried icing strands into sprinkles. I like to pick up a bunch of the long strands and break them like spaghetti.
Store the sprinkles in an airtight container.