Just as it is in classical French cuisine, roux is a mixture of flour and fat, usually butter or oil. The proportion is roughly 1:1, but I tend to use slightly more flour than oil; maybe 1-1/4 cups of flour to 1 cup of oil.
French Chef’s use this mixture to create gravies, sauces and creamy soups. It is the basis for many Louisiana dishes, particularly gumbo, but also etouffees, sauce piquantes, and more.
Roux is used to thicken gumbos, sauces, étouffées or stews, and in the case of a darker roux to flavor the dish as well. Dark roux has more flavor, a wonderful roasted nutty flavor, but tends to have less thickening power.
Preparation of a roux is dependent on cooking time; the longer you cook, the darker the roux. A blond roux will only take four or five minutes; a dark roux up to 20 or 25 minutes at high heat, or up to an hour at low heat.
Roux must be stirred constantly to avoid burning. Constantly means not stopping to answer the phone, let the cat in, or flip the LP record over, and if you've got to go the bathroom ... hold it in or hand off your whisk or roux paddle to someone else. If you see black specks in your roux, you've burned it; throw it out and start over.
When you're stirring your roux, be very careful not to splatter any on you. It's extremely hot, and it sticks. They don't call it Creole napalm for nothing ... I have a lovely burn scar on my forearm from last year's Christmas Eve gumbo, when I got sloppy with the stirring.
Certain dishes (like crawfish étouffée) would benefit from a butter-based roux, but if you're going to make a dark roux, this will take a long time. Butter roux must be cooked at low to low-medium heat, or the butter will scorch. Darker roux are better suited to being made with oil. If you know what you're doing, you can make an oil-based roux over medium-high to high heat, whisking like hell, and you'll have a beautiful near-milk-chocolate colored roux in about 20 minutes rather than an hour. Peanut oil works best for high-heat roux cooking.
Now, one not-so-bad idea is the oil-less roux, pioneered by Cajun Chef Enola Prudhomme. Basically, you just dump the flour into a cast-iron skillet and toast it dry, making sure to stir it around as you would a normal roux. I've never tried this, but apparently it works rather well, and is perfect for folks who are on low-fat diets.