This page explains everything about how you and your members can assign colors to themselves!
Every can use the /set color command. You will need to provide the name or the number of the color. Example: /set color name:Green or /set color number:1
Members can also get a color via a reaction color message. These can be created with /add reaction colors or /add reaction color. More information about how to create reaction color messages can be found on the Managing reaction color lists page.
Reaction color message example.