Proofread your work, to check for spelling and grammar mistakes. A publisher will almost certainly reject a manuscript which is riddled with errors. If necessary, send to friends or colleagues and have them check for errors. They may spot mistakes you have made.
Send your story into as many publishers as possible. Search the Internet to find the addresses and names of publishers in your area who you can send your story to. Most publishers will not charge you a fee for publishing, but will instead pay you an advance, or royalties or both. You may have to send to a number of publishers before you receive a response. It is best to research the specialties of publishers before sending in your manuscript.
Send your story into a magazine or journal. Many publications look for short stories to publish. Search the Internet for magazines or journals which are related to your story. If your story is long, then you may be able to condense it, or select a specific chapter to send in. This may generate interest in the wider story, which can then be serialized. Be sure to include a word count at the top of your submission, or it may not be read.
Publish your story on the Internet. If you have a blog, then you can publish sections of your story for free. Send the link to your friends, and post on the blogs of other writers to ensure that your story is read by as many people as possible. You may be spotted by a literary publisher if your blog generates a lot of interest.