A roux, like a slurry, is a method for adding starch to a liquid with the purpose of thickening the liquid. This is a basic technique, albeit not necessarily easy. There are a few guidelines that one should observe to obtain success with the process. If you add flour or cornstarch directly to a hot liquid, it will lump and will fail to disperse evenly throughout the liquid. The end result will be less than desirable, and your sauce will not have a velvety texture, as hoped for. With a roux, we heat the starch separately, from the hot liquid, before combining it with the hot liquid. Compatibility with the temperatures of both facilitates the combination processes and helps create a smooth sauce.
Simply take equal parts of fat and starch, and cook both together in a saucepan (about 2-3 minutes), over medium heat, stirring continually while the starch is cooked in the fat.
Butter and flour are a fool-proof roux, but chicken fat, bacon fat, and olive oil also work quite well, and should be considered when you have them on-hand. Just consider what you want the flavor of the sauce to finish with.