Béchamel is also known as a white sauce. In its most basic form, it consists of milk which is thickened by a roux.
To start the béchamel, first melt the butter in a small pot over medium-low heat. Add the flour and whisk to form a white roux that has a medium consistency. Cook the roux for about 1 minute; it should not turn color.
Slowly temper in the milk, a bit at a time. To prevent lumping, let the milk heat up a bit before whisking. Once all of the milk has been incorporated, gently simmer uncovered for about 10 to 15 minutes to cook out the starch flavor.
The béchamel should have a medium consistency (thicker than a sauce). Strain if desired. Season to taste.
You can add flavorings/aromatics to the béchamel by sweating items such as onions, garlic, herbs, etc., at the beginning with the butter. This softens and extracts flavor. Add the flour to the mixture and continue with the recipe. Strain the aromatics once done. Season to taste.