It's for a story I was writing, and in the story, there's a section of the newspaper in which people can submit stories/poems/essays to, and good ones were chosen to get published on the newspaper. These people could get money for getting their work chosen and published. But I don't know how much they should get (how to calculate it? Like for example, 10 cents per word?), and do they just get paid, or do they need to sign a contract or something?
AFAIK, people usually don't get paid for that sort of thing. It's like a letter to the editor. The reward is getting your story/poem/essay in the paper. The small amount of money that somebody would get paid for a one-time short submission isn't worth the newspaper's bother.
But, if it's a weekly contest, then the newspaper might want to increase interest by having a small monetary reward also. However, whatever amount you choose could easily sound silly in 10 years, and would probably not translate well to other countries. So, I'd suggest that your story's newspaper offer something to the winners like a one-month subscription, or a basket of groceries (sponsored by the page's advertiser, a local grocery store).
Note: This question seems familiar.