How do you keep from cotton yarn color from fading into lighter colors

Did you dye the Cotten yarn or buy it? ....you need something that will set the color, Depending on the dye type. With some dyes it’s vinager solution, others not. See if the manufacturer has a web site with information about the yarn and how to wash it.

I don't know if this applies, but it's suggested to put a white towel (maybe cloth) in with your luandry, help clothes not fade.

Wash it first. and don't wash at too higher temp.

You can try adding vinegar to the wash water to set the color or there is a product by , I believe, Shout puts it out called Color Catcher that you add to the wash. It catches colors that would otherwise bleed.