It can be done a couple of ways but basically, everyone receives/picks a prompt, writes a fic to that prompt and then loads of fic is posted.

Some ficathons have monthly-ficathons, where for every day of the month, there's a different prompt, and at the end, the people who finished all/the most prompts get a little banner.

Then there are the ones that work like Secret Santa - you ask for a fic and then write a fic for someone else. And the ones where you claim a single prompt from a list.

/ends ramble.