There are hundreds of "ezines," or online literary publications; many are good, some are not -- but of course, to each his own!
Some of the online literary sites are companions to traditional print journals. Many of these have been around for decades; some are "establishment" publications, and others are more open to new and young writers.
For many print publications, you still need to snail-mail your submissions; but usually, they provide guidelines online for how to get through the door. Look for "Submission Guidelines" or "Submit" on the site.
Many, though, allow emailed submissions; there are still guidelines to follow -- carefully, to avoid going unread altogether. Some also have a Submissions Manager tool -- you upload a file and can track it through the Manager.
My recommendation is to do a lot of reading of these ezines (and print journals) before submitting any or your own work. It's all subjective: editors are not gods, but they sometimes act like they are. Check the guidelines regarding format, number of pieces, method of submission, aesthetic preferences, genre preferences, submission period, simultaneous submissions, and other matters.
Borders, Brazos Bookstore, Barnes & Noble carry some print journals. Also, the public library has some, but to see the greater number, go by the UH, TSU, or Rice libraries, and ask the librarian (or search the catalog) to find call numbers for most literary journals. Give yourself an afternoon to browse, and find ones you think are worthwhile -- for reading, perhaps subscribing, and eventually, for submitting.
Here is a site that lists a lot of lit mags:
...but google "ezines" or "literary journals" yourself, and you'll find specific sites as well as other directories that are worthwhile. None lists everything; so, search a few, at least.
And here are a few online mags worth browsing:
Born specializes in multimedia presentations;
...experimental work, for the most part;
..."establishment" writers -- the traditional Creative Writing world, online -- but you'll find some of the best living American writers here;
...young writers, heirs to the Establishment;
American Poetry Review -- the Establishment, and then some -- this is the main print publication for academic poetry;
...another key player in academic poetry, but a bit more open, perhaps;
Callaloo specializes in African American writing;
...one of our local journals -- but of national reputation; run by the grad students, but professionally;
..."creative nonfiction" done concisely;
...the anti-establishment, but successful enough to have become Establishment Alternative; this is a clearinghouse site, so take time to explore;
...a wide range of academic and more freewheeling writers.