There are really no hard and fast rules about making a roux in south Louisiana. Every cook has his or her own method. Some will tell you that a roux is made by combining equal parts of oil (usually vegetable oil, though in the old days, lard was used) and all-purpose flour in a cold, heavy pot and stirring slowly and constantly over medium heat until the desired color is reached. Then again, some cooks choose to heat the oil a bit before adding the flour and continuing with the cooking. And yet others may prefer heating the pot before adding the oil-flour mixture all at once. There is also debate about the ratio of oil to flour. Some like more oil; others prefer more flour.
It really doesn't matter how it is made. What does matter is that, should it burn, it's best to throw it out and begin again. A burnt roux will make whatever dish you are preparing taste awful.
The roux that is made in south Louisiana is the base for many of the local dishes, such as gumbo, stews, and some gravies. The color of the roux can range from blond to medium to dark, depending on what type of dish you are preparing. For example, a crab stew may be made with a blond roux, while a dark roux is used for most gumbos.
Here is Eula Mae's technique: "I usually prefer peanut oil because it doesn't have an odor and it doesn't smoke. But corn oil is also acceptable. Some cooks like vegetable oil, and that's okay too. Everyone has his or her preference. I like a little less oil than flour because I like a thick roux. I like to use a cast-iron pot, but if you don't have that, any heavy pot that heats evenly is fine. The amount of time that it takes to cook your roux will depend on the type of pot. I like to cook my roux over a medium heat. And once you get it going, it shouldn't be left unattended. You don't want to burn it because you'll have to start all over again."
3/4 cup peanut oil and 1 cup all-purpose flour
Heat the oil in a heavy (preferably cast-iron) pot over medium heat for about 2 minutes. Add the flour and blend. Stir slowly and constantly. To make a blond roux, the color of sandpaper, it will take about 8 minutes. For a roux the color of peanut butter, cook for about 12 minutes. A dark roux, the color of chocolate, will take 15 to 18 minutes. As it cooks, the roux will thicken.
Eula Mae always says to make the roux a little darker than you want it because once the vegetables, broth, or water are added, it will lighten up just a bit.
Recipe from "Eula Mae's Cajun Kitchen Cookbook"