It's a pretty simple premise: people post anonymous requests for fic, and then others fill the prompts. There is no limit on prompts, and no deadlines on filling them. The idea is that the meme just goes on and on as long as people are willing to write. The Star Trek meme is hugely successful and regularly turns out excellent fic.
See the rules here.
Any questions, just ask here.
Feel free to contact the mod through PM or at ai_kinkmod