Ingredients
Butter
Flour
Milk or stock.
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Quantities will vary depending on the volume of sauce required and the desired thickness.
The standard rule is one butter to one flour, i.e. one tablespoon each to half a cup liquid. Two tablespoons of each would require one cup of liquid. For a white sauce, at least half the liquid should be milk. You can make a velouté following the same method and using only stock.
Preparation
Melt butter in a saucepan over gentle heat. Add flour, stirring to combine. You want the flour and butter to come together in a paste. If it is too grainy, add more butter. If it is too thin and you can see pools of butter, add more flour. This paste is called a roux.
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Cook the paste for a few minutes on a gentle heat. You want to cook the flour out but not brown the paste. Lift the saucepan off the heat if required to lower the temperature. Once the paste has cooked, it will be slightly bubbling and leaving a film on the bottom of the saucepan, turn off the heat and add the milk a dash at a time. Stir well after each addition. The paste will start to thin and then seize. This reaction is normal. Keep adding milk or liquid, stirring after each addition. You want to bring the sauce back to liquid consistency. Wipe the sides of the saucepan down and scrape any lumps off the stirring implement. Stir any lumps back through the sauce.  Â
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Turn the heat back on low and stir continuously as the sauce thickens. You will need the sauce to be bubbling to signify it is fully cooked. If it gets too thick, add more liquid. You can speed up the process by turning up the heat, but as soon as the sauce starts to thicken (you can see the bottom of the saucepan when stirring), you will want to turn down the heat to avoid lumps.
Notes
This recipe is the basic white sauce. You can then flavour as desired. Cheese, mustard, truffle, green peppercorns, vinegar, cayenne pepper, and paprika all work well, and you can often use a combination. It will depend on your end use. You can also control the thickness at the end by adding more liquid to create more of a pouring sauce. The same method can be used for pan gravy, making a roux in the cooking pan and adding the cooking juices to make the gravy.