When you say "publisher," I think novels. I too am confused; is this a novel or a short story? Or do you have a novel already and are looking to publish a short story too?
For short stories, check your contract. Some magazines will give the rights back to you upon publication or after a period of time. One of my shorts had a three-month exclusive period, after which I was free to submit it elsewhere. Others have reverted the rights to me as soon as the issue was published. The story will be publicized through the magazine's normal outlets, but many (again, check your contract) will let you link to their website from your (or from you AW signature) or post a reprint on your webpage (if you have one).
For books, check your contract. Self publishers and publish-on-demand (POD) publishers will put all of the publicity and marketing on your shoulders. I have no experience promoting a novel (although I have one published POD), but many people will have a website for themselves or even for the book, will spend time on the phone with bookstores, libraries, reviewers, etc. This is, by all accounts, not a very rewarding experience. It seems to take prior knowledge of the industry and outlets.
I hope that at least gets you started. Feel free to clarify your situation and perhaps we can give you more direct input.