Everyone can vote for up to 6 stories. For that you can assign each story you're voting for one of the numbers 1-6. That's the number of votes that'll get counted for it from your vote. Using ShadowStepper, who posted just above you as an example, he'd give 6 votes to I, Panacea, but only 1 to Trump Card.
At the end of the voting period Ack uses a program to count out the votes from that period and the story that has the highest number of votes gets a new chapter.
Then that winning story's votes get reset to 0, while all the other stories keep their votes, so that the most popular story doesn't win again and again.
Hope that clears things up.