The bechamel sauce
To make 4 cups of bechamel, put 4 1/2 cups of milk (whole if you want the richest sauce, but you can also use low-fat..skim really doesn't work well) in a heavy-bottom pan. The extra 1/2 cup is to account for evaporation. Throw in 1 whole peeled onion stuck with 1 clove, and 1 bayleaf. Bring this up to heat and simmer for a while (at least 15 minutes) so that the milk becomes steeped with the flavors of onion-bayleaf-clove.
When the milk is piping hot and suitably steeped with flavor, make the roux using 4 Tbs butter + 8 Tbs flour, as described above. Now add the milk to the roux, one ladle at a time (straining out the flavoring incredients), and mix vigourously until the roux and liquid are amalgamated. Do not add the next ladleful until the mixture is smooth. Continue adding the liquid until the sauce is the thickness you require. Season with salt and pepper (white if you must have a pure white sauce, but I always just use black) and a little grated nutmeg
What if your bechamel (or any other roux-based sauce or gravy) is lumpy despite all your precautions? There is one thing that will fix any lumpiness: an immersion or stick blender. It's not just for pureeing veggies in soups or whirring up your powdered protein drinks! A few seconds of blending with this tool will de-lump your sauce in no time. A basic stick blender such as this one doesn't cost much, takes up very little counter or drawer space, and is endlessly useful. If you don't have a stick blender, you can try to get as many lumps out of as possible by vigorously mixing the sauce with a whisk, and then if you want a perfectly smooth sauce, simply strain it through a sieve.
Now, you have conquered roux and bechamel - what to make with it? Stay tuned.
Addendum 1: for a very traditional bechamel, the onion (or shallot) is sautéed in butter along with a small amount of chopped veal, but I find that for most modern dishes requiring bechamel this is not really necessary.
Addendum 2: In Japan, 'white sauce' is available in cans. I don't know why other countries don't have canned bechamel, since t's so useful.