So as a graduate student, you are always expected to get your own study published. This could be a frustrating process.
First off, make sure you can publish your paper in the correct category. When you start off trying to get your paper published, you should start looking into and researching things that are already published in your field. Make sure your paper is different from others.
Then, ask yourself if you're addressing questions and concerns within the studies that others have not. Check out how others have written their papers. Parameters such as format, vocabulary, etc. should be taken into consideration.
Having an intimate knowledge of the existing works in your field of study will definitely give you an upper hand when submitting your paper. Get input from others on what they think is important.
Actually, before you ask how to publish a paper, you should first make sure that your manuscript is ready to go. That includes typing a rough draft, getting it proof read by at least two different people. Multiple proof readers can catch things that maybe the other person or you didn't. Only when you've made sure your paper is thoroughly revised (maybe even for several times), should you try submitting it for publishing. Remember that you may be rejected the first time, or even the first few times. Don't give up. Eventually someone will accept your publication. This is a big way to publish a paper.