HOW TO MAKE A ROUX
Roux is basically a mixture of fat and flour, cooked, and used for thickening sauces, soups, or stews. The point behing cooking flour in the fat is to keep the flour from lumping together before adding to the liquid, and to destroy a protein that would otherwise impair the thickening ability of the flour. Of course, cooking also creates some taste molecules that give the flour a more interesting flavor than the taste found normally in raw flour. The color of the roux is also affected, especially depending on the time of cooking. The longer the time, the darker the roux becomes, but also the less thickening ability of the flour there will be. However, the darker roux has more flavor, so depending on the needs you should find a balancing point between the two extremes of color.
Roux is prepared with any white wheat flour available, preferably a high-starch flour (normally a simple all-purpose flour). The other ones that you may have access to are cake flour and bread flour. Cake flour has even more starch in it and therefore will thicken the dish more, while bread flour is the least starchy of these three wheat flours.
Fat that is used in roux is usually butter, due to its nice taste, but it is preferable to use a clarified butter since it will not burn that easily. And, as said already, the more temperature you can apply to the flour the better the taste will be. If you want to use another type of fat, you can try any vegetable oil (olive oil or corn oil) or maybe some type of animal fat. The choice of the fat should be applied to the type of dish you are making, since each fat type will provide a different kind of flavor.
How is roux made? Place a pan over a moderate heat, and throw in three parts flour and two parts fat. Stir continuously so it doesn't scorch and continue to cook until it reaches a desired color and texture. The final product should be fairly shining and look like a moist flowing lava (well, kind of!). Anyway, it shouldn't be greasy and it shouldn't be dry. If it is, adjust with more flour and fat, respectively. Your roux will go through different stages of color and flavor, as it continues to cook. So, you will first get a yellowish roux, then a more orange-blond color, then a red-brown, and lastly a dark-brown roux. The flavor will also become enhanced with the darker color. Stop cooking when you reach the desired color and taste and use it in your main dish, or store in refrigerator for later use.
To combine your roux with a dish you don't have to heat it up, as it can be added to the dish either hot or cold. However, make sure so you don't mix it into a very cold or very hot temperature to avoid lumping or spatter, respectively. It is nevertheless easier to combine a slightly warm roux with the liquid, since the fat is not that hard as it is in the refrigerator. Once you've added the roux, heat the liquid to almost 100 C/210 F to start thickening the dish. If you want it to become even more thicker, you can even reduce the liquid. That's it for the roux!