What sort of publishing? Are you trying to get it published into a newspaper or literary magazines, or publish like a book would be published? Would it be something you want to copyright? Would it be something you want to sell?
The answer to your question really depends on your answers to the above questions.
If you want to publish into a magazine, all you need to do is find a magazine that publishes literary works, and submit yours. The more local, the easier it is to get it in the magazine. Magazines that publish literary works generally have a limit on the size of the work, and may or may not reserve the right of editing your work. I have gotten poems published this way, and it is very easy as long as you know where and how to submit it.
If you want to publish it as a book would be published (actual publishing, such as you would do if you want to sell copies of the work), the process is much more complex. You have to find a publisher that will publish your work. Many publishers will not even look at your submission if you don’t have an agent. Agents cost money, and don’t guarantee that your work will be published. If you do get a publisher to accept your work, you can expect them to take a large part of profits from the sale of the work, along with many of the legal rights to the work.
If you do not find a publisher, you can publish the work yourself. You can keep all rights and profits, but you have to do all of the work of finding a place to print the book and a place to sell the book. I would not recommend this unless you think that it is worth the trouble.
Even if you do not plan on publishing the work, it is still possible to copyright the book, but it does cost money.
I hope this helps.