One is having a written, agreed-on proposed standard for that breed or color. Something that at least half the population follow by quite well.
Another is I believe 5 years background. I believe you need several breeders with 5 years experience on the breed or color to vouch for it.
Oh yeah, and once it gets known enough, there comes a time of assessment where at a show, many people may present their bird of that color or breed and have it assessed. If there is a good enough majority or uniformity shown, it will pass on go on to the next step of acceptance. For example, French Marans are awaiting to be in the APA, and part of that are meets at specific dates/locations where a bunch of birds of the specific colors (first is Black Copper, next I believe is Wheaten) are all assessed for uniformity and type that matches the proposed standard.