The most basic method of making gravy uses a wheat flour slurry or a wheat flour and butter roux to thicken the pan drippings when you cook a chicken, turkey, or roast. But you can substitute some other starches with varying results.
Flour Gravy Thickener
With a roux, you start by cooking the flour and the butter together until it reaches your desired color, with a lighter roux more appropriate for white or country gravies, and progressively darker hues for turkey, chicken, and beef gravies. Most home cooks stock all-purpose wheat flour, making this method a convenient one. But flour adds a cloudy appearance to the gravy, so it may not always be the best choice. It also does not have thickening power of other starches, so it needs to boil for about three minutes. Some styles of gravies and sauces don't benefit from the high temperature and longer cooking time required.
Alternative flours don't have the same starch content, so they do not all make appropriate substitutes for wheat flour as a gravy thickener. Sweet rice flour seems to consistently perform in place of wheat flour as a gravy thickener, however.
Cornstarch Gravy Thickener
Cornstarch results in a lighter, more translucent gravy with a glossy sheen. Chinese and other Asian recipes frequently rely on it to thicken sauces.
To use cornstarch as a gravy thickener, start by making a slurry of equal parts starch and cold water, stirring until it looks completely smooth. Then slowly incorporate it into the pan drippings, whisking continuously. Cornstarch turns lumpy in hot liquid, so don't skip the slurry step, and be sure to add it slowly while you whisk to thoroughly integrate it into the drippings.
The starchy flavor can linger unless you cook it long enough, so simmer the gravy for a minute or two after you add the slurry. Be careful not to overcook it, though, which can cause it to turn runny. Remove a cornstarch-thickened gravy from the heat before you add acidic ingredients. One tablespoon of cornstarch thickens 1 1/2 to 2 cups of gravy.
Arrowroot Gravy Thickener
Arrowroot results in a smooth, transparent gravy with a light texture. The nearly flavorless starch does not requiring cooking to remove a raw taste. It makes an excellent choice for sauces using eggs or other ingredients that should not be boiled since it thickens below the boiling point.
Gravy thickened with arrowroot does not hold well, however, and you cannot reheat it. You should finish your gravy with an arrowroot slurry no more than 10 minutes before you plan to serve the meal. Extended high heat and vigorous stirring nullify the thickening properties of arrowroot; if your gravy suddenly turns soupy, you've gone too far. Use 2 1/2 teaspoons of arrowroot per one cup of cold liquid for a medium-thick sauce.
The Complete Book Of Sauces can help you brush up on your saucier (a fancy restaurant kitchen term for the chef responsible for the sauces) skills even more.