Exact amounts of flour and fat for the roux will depend on the specific recipe, though the ratio of flour to fat is usually 1:1.
Method #1: Stove-top This is the traditional method and how most recipes will tell you to make your roux.
Start off in the traditional way by cooking the flour and fat over medium heat until they form a smooth paste. Next, lower the heat and cook until the roux is a dark, chocolate brown. Stir very frequently and scrape the bottom of the pot to avoid burning. This should take an hour or more.
Method #2: Oven While not the traditional way of making brown roux, we feel that the oven method is easier and more fool-proof, plus you don't have to baby-sit the roux quite so closely.
Preheat the oven to 375°. In a dutch oven or other oven-safe dish, start the roux on the stove-top by cooking the roux over medium heat until it forms a paste. Move the dish to the oven, uncovered, and cook for ten minutes. Stir the roux, being sure to scrape the bottom of the pan. Continue cooking and stirring every 10 minutes until the roux is a dark, chocolate brown. This should take an hour or more.
Gumbo is definitely the most popular dish using a brown roux. Try these recipes: