Autosexing requires the barring gene from both parents, plus a color of chick on which you can see the difference. It works because the barring gene is on the Z sex chromsome. Males have ZZ, females have ZW. So a male with two doses of the barring gene will show more white than a female with one dose of the barring gene. The "more white" usually means a larger head spot at hatch (easiest to see on black chicks), and can also mean lighter color chick down (on the brown striped pattern of a Bielefelder or Cream Legbar), as well as growing feathers that show more white. (Not every gene has a dose effect like that. But barring does, which is what makes it useful in this case.)
Autosexing breeds true. For example, you cross a Bielefelder rooster with a Bielefelder hen and get Bielefelder chicks, who can be sexed by the color of their down.
Another way to have chicks that can be sexed by color is with sexlinks.
Sexlinks are a one-time hybrid. There are created by crossing one kind of rooster (example: Rhode Island Red) with a different kind of hen (example: Light Sussex or Barred Rock). The chicks can be sexed by color, but when those chicks grow up they cannot be used to produce more sexlinked chicks.
Sexlinks work because a hen gives her Z chromosome to her sons, and her W chromosome to her daughters. A rooster gives one of his Z chromosomes to every chick. Clever choice of parents means that the daughters show a recessive gene (inherited from their father.) Sons show a dominant gene (from their mother), while also carrying the recessive gene (from their father.)
Several genes work for sexlinks, with the most common being silver/gold and barred/not-barred. (Silver and Barring are the dominant traits, gold and not-barred are the recessive traits.)