A roux, as you know, is a cooked mixture of generally equal parts flour and butter, that is used to thicken soups, sauces, and stews. The butter is melted gently, the flour is added, and the mixture is stirred and cooked over medium heat to remove the taste of the uncooked flour and to begin the roux’s thickening process.
The longer you cook the mixture, the darker it becomes. If you cook 2 Tbsp of butter and 2 Tbsp of flour for 2 minutes, you’ll have a white roux (barely beige); if you cook them for 4 minutes, you’ll have a golden roux or blond roux (pale golden). The more roux you make, the longer you have to cook it to get it to the right stage. If you use 1/2-cup each of butter and flour, it will take 8 minutes for a white roux and 12 minutes for blond.
A brown roux is the ultimate stage in the roux kingdom, and is often made with lard, beef fat, or drippings, and is cooked to a deep golden brown. For many Cajun and Creole dishes, a roux may be cooked for an hour, until it reaches mahogany brown.
Avoid the temptation to use higher heat to get the roux done faster - an overheated roux loses half or more of its ability to thicken, and there are those among us (and we're being honest here) who have burned more than one roux by impatiently turning the heat up too high.