This is premature for us, perhaps, but all the same, it's worth considering ways of publishing your work when you feel it's ready. There are many ways to publish -- which, over the past fifteen years or so, has meant online as well as in print (well, we can include electronic media such as CD's as well, I guess -- and even live performance is a kind of publication).
Below is a link to information on an undergraduate-oriented literary journal; there are other types of journals, including online, and then there are more "commercial" or "popular" publications. It really depends on how you see your writing, your intended audience, and your concern about $$$. Literary writing doesn't pay much, or at all! It's for the "art." In our course, I'm focusing on the "art," but that doesn't mean your writer's sensibility has to be artsy -- just focused on matters of craft.
Anyway, here's a call for submissions I received from a former colleague; and below that, a web site that lists many journals, magazines, and small-press publishers (more on book publishing in a later post).