In the culinary world more often than not you have to add viscosity and body to something you are preparing, whether that be a soup, a sauce, or a stew. Luckily for the cooks of the world there are a variety of methods for doing just that. Each method has its own pros and cons as well as a preferred application. The most traditional and most commonly used methods is through the gelatinization of starches. Some other methods include reduction and adding an already thickened substance. When you thicken something your goals should be to avoid lumps, have a good clean taste that is not pasty or floury, have a good consistency and that it will not separate or break when being held.
One of the most classic methods, and generally one of the first taught is the use of roux. At its most basic roux is simply equal parts flour and fat (by weight) that have been cooked together to make a paste. Roux varies by color gradient ranging from white, blond, and brown roux. You achieve a darker color roux by cooking the flour and fat longer. The color of the roux plays a part in what you are using the roux for. White roux is used for things that are either white in color or where no added color is wanted. Dark roux is used in dark colored items, such as gumbo. Another important note is that as you cook a starch you remove some of its ability to gelatinize in liquid, so you will need more dark roux than lighter roux to thicken the same amount of liquid.
The procedure for making a roux is the same no matter what the color. First heat your fat in a heavy bottomed saucepan taking care not to burn it. After the fat is nice and hot add your flour. General purpose flour is ok to use, but pastry or cake flour work better for roux making due to the higher starch content. Avoid high gluten flour. Stir your flour and fat mixture until you reach your desired color. White roux does not take very long while dark roux can take several minutes. When you are cooking your roux it is important to watch over it and constantly stir it. Roux, especially when making dark roux, can go from tasty thickening agent to burnt disgusting mess in an instant. Burnt roux does not thicken anything and will make your food taste bad. A little trick I have learned for making dark roux without constantly watching over it is to put your roux on a sheet pan (cookie sheet with four sides) and put it in a 200 degree oven until you reach your desired color. A good roux will have a nice almost nutty smell and will be slightly stiff, nor runny.
When you have made your roux you can incorporate it into your food in two ways. You can let your roux cool down and add it to hot liquid, or you can add cold liquid to your hot roux. In either case it is important to stir vigorously with a whisk so that the liquid and roux are properly incorporated and you avoid lumps. After your roux has been added you need to allow your liquid to heat up to a boil. This will cook out any of the flour taste and allow the starch to gelatinize.
Another way to use flour and fat(butter) to thicken items is to make a beurre manié. Beurre manie is equal parts flour and butter, by weight, that have been kneaded together. The mixture is then whisked slowly into a simmering liquid to thicken. Unlike roux, the mixture remains uncooked and it generally added at the end of the cooking process as a finishing technique or as a quick thickener. The butter adds shine and flavor as it melts.
The next way to add thickness to liquids is to use cornstarch. Cornstarch is much easier to use than roux because the only thing you need to do to use it is to mix it with water to create a slurry. Once the cornstarch is completely incorporated with the water, just slowly stir it into hot liquid. The liquid does not necessarily need to be boiling, but it does at the very least need to be simmering. Unlike roux, cornstarch will have a more immediate effect. Cornstarch is used heavily in Asian cuisine. It gives liquids a glossy sheen that may or may not be desired. Cornstarch also has the benefit of having twice the thickening power of flour. However, liquids thickened with cornstarch are less stable as it can lose its thickening effects over prolonged heating. Also, products that have been thickened with cornstarch should not be reheated.
An alternative to cornstarch and flour as a thickener is arrowroot. Arrowroot is derived from the roots of several tropical plants and is similar in texture and appearance to cornstarch. In fact, you use it the very same way. You mix it with cold water making a slurry than whisk that into a hot liquid. Arrowroot has slightly more thickening power than cornstarch, is not affected by acidic ingredients or freezing, thickens at a lower temperature than flour or cornstarch and it has a more neutral flavor. Arrowroot however, does not work well with dairy products, producing a slimy texture when it does. Arrowroot also has a tendency to break down when overheated and is quite a bit more expensive.
When not using starch to thicken liquids you have some options at your disposal. The easiest is to thicken something by reduction. All this means is that you allow the liquid to cook down until it is reduced in volume. This method is especially useful for making sauces or glazes. Just keep in mind that when you are reducing something the flavor of your liquid is being concentrated into the remaining liquid. Another way you can add viscosity to your liquids is by incorporating an already thickened liquid or item to it. Many a time I have added tomato paste to a tomato based sauce or soup to give it the consistency I wanted. It is also not uncommon to add thickness using demi-glace to a sauce. Just keep in mind that your desired thickness will have to be based on what you want thickened and what you are adding to thicken it. You can't turn an au jus into a gravy with nothing but a reduction or by adding only demi-glace to it.
One quick final note about thickening. It is always important to try to achieve your desired thickness with whatever method you are using. However, if you over thicken something the solution is just to add more liquid so you get it to where you want it. You may end up with slightly more product that you had originally intended and you may have to adjust your seasoning, but that is better than serving a gravy when you just wanted a light sauce.