Do they submit it to journals similar to those of the natural sciences? If so, what are the major journals? Is there a peer-review process for submissions? Is there an online repository of papers similar to www.arXiv.org? Do you have to be a known contributor (or endorsed by a known contributor) to submit a paper, or can anyone do so?
In fact, I could ask the same question for any of the humanities. I really don’t have a clue how papers are published outside of the natural sciences.
Peer-reviewed publication is part of any academic discipline. For philosophy, this and this may get you started with journals, but I’m outside my field here and can’t help you tell the good from the bad.
Any academic field that’s worth a damn (and some that aren’t) will have its own peer-reviewed journals. One shortcut to finding the good ones is to see which are indexed by databases, like ISI’s Current Contents, which select the most highly cited journals. The master journal list for all ISI products is here; philosophy is in the Arts and Humanities citation index.