Potato starch has more thickening power than flour, doesn't contribute flavor of its own and acts instantly -- just about everything roux, or equal parts fat and flour, doesn't do. Potato starch doesn't need fat to congeal and gelatinizes at a lower temperature than flour does, so you need about two-thirds less. Since potato starch consists of pure extracted starch, it has nothing to get in the way of thickening, but it has nothing to support it, either, so you have to add it at the end of cooking and watch the heat to keep it from breaking down.
Portion about 1 1/2 teaspoons of potato starch for every cup of liquid, soup or sauce you want to thicken and place in a small bowl.
Add an equal amount of water, stock or broth to the potato starch. Whisk until a thick paste forms. Set the slurry aside or in the refrigerator until the sauce or soup is ready.
Cook the sauce or soup fully through and season it to taste.
Add the slurry to the sauce or soup while whisking briskly and constantly. Bring the soup or sauce to a simmer and turn the heat off.
Sir the sauce or soup once more and serve it as soon as possible.