People can write mystery stories for money by getting their stories accepted in magazines and anthologies (mystery or general fiction, online or print), or publishing them, either via self-publishing or through a publisher.
The Mystery Periodicals page on the Mystery Readers International website lists mystery-themed magazines that accept stories. According to Writer's Digest magazine, one of the best ways for people to find magazines or anthologies to submit to is by checking out the acknowledgements page of short-story collections. The page often lists which magazine first published a story. However, Writer's Digest notes that pay is relatively low for short stories.
Another way to write mystery stories for money is by publishing them. Some people opt for self-publishing, in which they (or someone they pay) are responsible for cover art, formatting and uploading. Royalty payments can be as frequent as once a month. With self-publishing, authors can publish their mystery stories individually, in collections, as novellas or as novels, and set the prices they wish to charge. Traditional publishing requires more time for a mystery novel to reach the market, sometimes as long as 18 months. In most cases, an author must first be accepted by an agent, and that agent works with publishers to find a home for a story.