Pretty straight forward, you sign up (I have a basic membership) and when you setup your profile, identify what you have and sell. I've gotten way more foot traffic through them than anywhere else. You'll get frequent mailings, mostly asking for money and you'll have access to their research and technical support. If you want to have a booth at Mother Earth News Fairs, you can generally get one for free as a member.
I use their logo on all of my labels that are appropriate. Few people know what that is but it's a great talking point and people who buy eggs feel more invested supporting rare breeds. I had fairly good luck selling heritage turkeys, but again it took some explaining and marketing. Before we were two people, I would process and sell mixed breeds and those that didn't make the cut and preserve the best breeders to hatch and sell poults. My preference for an eating turkey is the red bronze, so I would hatch out 20-30 of those every year and put them in the freezer for sale.
ETA: Here's their member page:
https://livestockconservancy.org/index.php/involved/internal/membership