Starch has been used to thicken dishes before kitchens existed, most often mixed with oil, which coats starch granules for a better meld. Cooking this mixture eliminates the raw, pasty flour flavor, and though roux means “red”, roux are cooked for varying lengths of time to different colors for different uses.
The best rule of thumb is one part plain white flour to one part oil, but I always use a little extra oil to make it more manageable. As to what kind of oil, that depends on what you’re cooking. Generally speaking, if you’re making a white roux, use butter (not margarine, dear hearts). Since butter will burn at higher temperatures, use vegetable oil for darker roux as in most meat dishes and seafood, adding a little olive oil (particularly in a gumbo roux) for whang. Use lard or bacon drippings for that authentic down-home flavor you need in gravies.
Yes, I know you can make a roux in the oven, or even in the microwave, but the stove top gives you much more control over the product. It also requires care and attention. A lot of people call roux “Cajun napalm” for good reason; it will stick to your skin and burn, so when you’re cooking roux, avoid any distractions, use long-handled utensils, and for heaven’s sake, keep your children under control or out of the kitchen.
Don’t use a high heat to make a roux: cook with a medium heat, and scrape the bottom of the pan to achieve an even color. If black specks appear, you’ve burned the roux, and you have to throw it away and start over. Never, never, never use a scorched roux; your gumbo, etouffee, or what have you will smell (and taste) like an ashtray.
Just like a slice of bread, a roux will toast; the longer you cook the flour, the darker the “toast”. It smells like popcorn cooking; at least, it does to me. Those of you who grill a lot may be familiar with the Maillard reaction, the reactions of proteins and sugars under heat that give meats and vegetables that roasted flavor. The same process is at work here. Cooking roux to different degrees of browning render different flavors and colors. They also thicken to a greater or lesser degree; the longer you cook a roux, the less it will thicken.
For white sauces—béchamel and dairy sauce variations—cook the roux only long enough for it to stop bubbling, not long enough for it to brown at all. When making a white roux for soups and gravies it’s better to use slightly more butter, but for a thicker, stiffer sauce such as one you might use to hold a casserole together, use more flour. As a general rule, you’ll use lighter roux for dishes involving poultry or fish, darker roux for beef or game as well as most gumbos, with the exception of a file gumbo, which traditionally doesn’t involve a roux at all. With experience, you’ll learn to customize roux to your cooking.