This is really for tudor rose, who is/was in academia, polishing her MA thesis, and wondering how I went about getting published and what she might do—but since a) I know this is kind of a popular question [g], and b) the answer I started to leave started to get rather long—I figured I'd put it in as a separate post.
Anyway, the answer is (as always) that it kind of depends. I did a _lot_ of freelance nonfiction stuff, back when I was a scientist--but I rather fortunately had an expertise in scientific computation, at a time when that was a) rather rare, and b) highly in demand, because of the huge new popularity of personal computers.
What I did to break into that market (not that this is _why_ I did it) was to a) start my own scholarly journal, called SCIENCE SOFTWARE QUARTERLY, b) write a comic book for Walt Disney's Educational Media Department, titled NUTRITION ADVENTURES WITH ORANGE BIRD (I got that job because I was already writing comic book scripts for Disney, and when the Educational Media person called the comics editor looking for a writer, he kindly gave her my name. Tip #1: the more people who know you and what you do, the easier it is to get jobs), and c) wrote a brief note to the editor of BYTE magazine, enclosing a copy of "Orange Bird" and a copy of SSQ (with my name as founder and editor-in-chief circled on the masthead, and checkmarks next to the articles I'd written in the Table of Contents)
The note just said, "Dear Sir—as you can see from the enclosed, you won't find anyone who knows more about scientific and technical software than I do, and at the same time, can write to appeal to a broad popular audience. Yours truly…. P.S. I've never missed a deadline in my life."
OK, this worked. [g] I got an immediate assignment from BYTE, then used the clip of that article to get assignments from InfoWorld and PC Magazine—and with published clips from the Big Three (as they were then), I could pretty much write for anybody in the field of personal computing—and did, for several years. Within a year or so of beginning my freelance career (mind, I still had a full-time job as a university professor), I was making just about as much from writing as I did at the university (which is mostly an indictment of how badly universities pay their assistant professors).
Now, I really don't know whether tudor rose's thesis is in an area where there's a lot of publishing interest, or extant periodicals. If not…then your best bet (if that's the material you want to publish) is probably to try to produce a book-length manuscript, oriented to the popular market if you can (much better sales potential), but otherwise as a scholarly book—which is not likely to make you much money, but will establish your credentials, ala my SSQ/Orange Bird strategy. [g]
If there are periodical markets for your material, though—perhaps you could write articles based on your research for magazines like Archaeology, or The Smithsonian. Essentially, what you want to do in the beginning is to get into print. Nothing makes an editor want you, like proof that some other editor has already wanted you. And short articles like that could form a useful credential to accompany a book proposal.
One of the nice things about nonfiction is that it's possible to sell a book without actually writing it. You can put together a proposal for the book, indicating what material it would cover, who the potential audience would be, how long it might be, and an idea of how it might be structured—accompanied by things like your cv (if that's relevant), or any published material you might have (which indicates a) that you can write, and b) that there is some interest in your topic).
You can't, btw, sell fiction this way, unless you're already a well-established author. That's because no one can tell, from a proposal, whether you can really tell an engaging story or whether you know what a good novelistic structure is, or whether you have good characters. So you do (with very rare exceptions) need to have a finished manuscript (and I do mean finished, not, "Oh, surely the editor (who buys this for a million dollars) can tidy up all those pesky little grammar things, and I never paid enough attention in school to know what they're even called, hahahaha…" Stay tuned, btw, for an upcoming rant regarding homonyms and prevailing ignorance thereof. As a corollary to which, if you'll pardon my mentioning it, the male protagonist of my books is J-A-M-I-E. Not "Jaime". But I digress…) in order to sell a novel.
Anyway, tudor rose—the first step would be to look for markets that publish the material you're interested in publishing. Do you have a subject that can be adapted to magazine articles or other popular forms? (I'm not addressing online means of publication here, just because I've never done that, and it would take awhile to poke around and consider things. Also, I've never met anyone who's actually made money by publishing things online, and I think that's probably one of your eventual goals. [g]) Is it a subject that has no particular popular aspects, but is hot academically? There are lots of university presses and academic book publishers.
The most important thing—as always, in anything to do with writing (well, anything else, for that matter)—is persistence. Start looking around, and keep working.
Oh—and good luck!