One of the characteristics of a good sauce is its velvety smooth consistency—not too thick and not too thin. The traditional standard by which this is measured is that the sauce should "coat the back of a spoon." But unless you're in culinary school, you don't need to worry about this. Ultimately, how thick you want your sauce to be is a matter of preference.
Also, if you're following a recipe, you shouldn't have to worry about thickening your sauce. Just follow the recipe and it should turn out right.
But suppose you're just winging it rather than using a recipe? This assumes you have some basic knowledge of how to make a sauce, the common thickeners that are used with each type of sauce, and that you used a technique appropriate for the sauce you're making, but it simply turned out too thin. If that's the case, the solution is pretty simple.
Thickening Sauces By Reducing
To thicken a sauce that's too thin, your best bet is simply to reduce it, which means letting it simmer uncovered to evaporate excess liquid. Keep in mind, a sauce that might seem too thin in the pot after the first cook, will thicken up after a few minutes off the heat. So you might not need to thicken your sauce at all. Let it sit for 10 minutes and check it.
If your sauce is still too thin, reduce it. To do this, leave the lid off the pan so the liquid can evaporate. Again, the sauce will continue to thicken for a few minutes after you take it off the heat. Check it again and repeat until it's thick enough for your taste.
Most often, reducing the sauce is all you'll need to do. This technique is preferable to trying to add additional thickener, which can cause the sauce to over thicken. Whereas if you reduce a sauce too much, adding more liquid to thin it is an easy fix.
Thickening Sauces With Starch
Incorporating starches is one of the most common ways of thickening sauces. And the most common technique for doing that is with roux. Sauces like bechamel, veloute and espagnole use this method. Thickening with roux happens at the beginning of the process, so you generally wouldn't use roux to thicken a sauce after it's made.
Roux is a mixture of fat and starch that is cooked for a while before gradually stirring in liquid. Typically, roux is made with butter and flour, though it can be made with other fats, like lard or oil, and other starches, including gluten-free ones like rice flour. And while plain white flour is most common, you can absolutely use whole wheat flour. It will produce a darker roux, but it will work just the same in terms of thickening.
Roux works because heating a starch causes it to absorb liquid. This gives the sauce a uniform, smooth consistency, as opposed to the lumpy mess you would get if you simply added dry flour to a liquid. The fat keeps the starch granules separate while the starch is cooking.
Finally, unlike roux, beurre manie involves combining raw flour with whole butter to form a paste, then gradually stirring bits of this paste into a liquid, usually a soup, to thicken it. In a pinch, you can use this technique to thicken a sauce that is too thin, although for a home cook, reducing it is still your best bet.
Another way of using starch to thicken a sauce is with a cornstarch slurry. Cornstarch gives sauces a glossy sheen, like in sweet sauces and pie fillings, as well as in many Chinese sauces and stir-frys. Combine a small amount of cornstarch with cold water to form a slurry, and then mix that into your simmering sauce. You can also make a slurry with other starches, like arrowroot or tapioca, especially if your sauce is acidic, since acid interferes with cornstarch's thickening ability. For dairy-based sauces, use cornstarch or tapioca, as arrowroot mixed with dairy will turn slimy.
Thickening Sauces With Egg Yolks
Egg yolks are another common sauce thickener. Sauces like Hollandaise, Bearnaise and mayonnaise are made this way. The basic technique is to beat the yolks until smooth, then slowly whisk in the liquid oil or butter. If one of these sauces is too thin, your best recourse is to start with a new egg yolk, and gradually whisk in the original sauce, rather than adding an additional yolk to the sauce.
You can add egg yolks to a sauce to thicken it, by first creating what's called a liaison, then adding this mixture to the sauce. The most common type of liaison is a mixture of egg yolks and heavy cream. To do this without cooking the egg yolks, you temper the liaison by whisking a small amount of the hot sauce into it, then gradually adding the warm liaison back into the main sauce. The classic Allemande sauce for poultry is made this way.
Thickening Sauces With Purees
Finally, you can thicken a sauce with pureed vegetables. This technique is usually reserved for thickening soups and stews, but it can work for sauces as well, if you don't mind a coarser consistency. Cooked pureed rice or mashed potato will add thickness, but any pureed vegetables or legumes will also work. Adding tomato paste, if it's appropriate for the sauce, is basically a version of this technique, and will also work.
Finishing Sauces With Butter
Butter does not provide any thickening to a sauce, since it is made of just fat and water. But a chunk of butter, salted or unsalted, swirled into a sauce at the end, can temporarily emulsify a sauce, while adding richness and sheen, all of which are good things.