Define Your Goals.
"Breaking into professional writing" is a very loose definition. It could mean somebody who's only ever published a single book or a single short story; it could be somebody who publishes regularly but is widely held in low esteem; it could be somebody who self-publishes eBooks through Amazon; it could be a respected journalist or a guy who starts a poetry ezine.
And it's hard to say, right at this moment, which of these will eventually be right for you. You don't need to pick your eventual achievements right now. You do need to understand what it is that you're after, and what it is you want to spend your time working on. Obviously, some goals are more likely than others. Doesn't mean you can't shoot high, but don't be devastated if you can't reach 'em, either. Some goals include:
- Writing for yourself. That's something anybody can do; if you truly gain satisfaction from this, then you're doing well - no matter how poorly you might fare with your career (over which you have relatively little control), you are still finding satisfaction in the writing itself. People who don't have this goal are, shall we say, even less likely than others to cope well with the frustrations of the publishing industry and the state of the market.
- Getting Your Work Out. This is a common desire for writers - to have their work available to the public. (You touch on this yourself, in your cautious hope that you have a potential appreciative audience.) Nowadays, it is extremely easy to have your work technically available, with a slew of respectable options for internet publication, ebooks, and print-on-demand services. However, the vast majority of such works languish in obscurity; moving to higher steps of mild popularity, word of mouth, placement in brick-and-mortar bookstores, etc., are much more difficult. They generally depend on some combination of skill at the craft, and promotion/career abilities (e.g. getting a publisher to move this forward for you).
- Recognition. You want your ability and work recognized in some way. This isn't necessarily "being famous" or "people liking your work," just to be noticed and for your work to be appreciated (possibly by a very small group or an insider crowd of some sort) on its own merits.
- Fame and Fortune. Most creative types would love to become the rock stars of their own personal field. But this is really a pie-in-the-sky dream - the number of authors who achieve even modest popularity is miniscule; the ones who actually become household names, who earn serious money off their work, etc. is even more discouraging. This is also one of the elements that is pretty much entirely out of your own control - unless you know how to transform yourself into a wildly successful phenomenon, in which case you're already pretty darn savvy.
This is really the core of it all.
Lots of people are more interested in the process, in the industry, in the social scene - but they aren't actually writing. The only way to get in is to produce great writing. So by definition, you've got to be (A) productive, so you've got actual work to hawk, and (B) great, and the only way to get great is to practice, practice, practice.
Develop Your Craft
Writing is a craft and a profession; you want to push your boundaries and grow as a writer.
- Read books and essays on whatever aspects of writing interest you, on whatever you feel you need most, on things you feel like you could do better on. There's a lot of great, inspiring, and helpful resources out there.
- Be a voracious reader - don't isolate yourself from the field you want to contribute to. Know what's going on; maintain your sources of excitement, inspiration, and respect.
- Get feedback on your writing - that's the best way to understand where you're doing great and where you need work. Be able to take criticism well, and seek out those who can give you honest, constructive criticism.
- Give feedback to others - that's a great way to improve your own writing, and become more aware of possible flaws and of technique abilities.
All this being said - these should all be secondary to actually writing.
Learn the Industry
Navigating the publishing industry is a huge curveball for many writers - it's an entirely different skillset than what they're using for the core of their profession (which is actually writing, for those of you who haven't been following along). So somebody might write a great book, but not know how to find an agent, or mess something up with publishing rights, or fall prey to a scam, or try to e-publish and make a hopeless mess of it.
At low-intensity, follow what's going on in the industry. You can follow along with industry blogs by agents, editors, self-publishers, what-have-you - you'll seek these out depending on your personal field of interest. I won't list blogs here, except for Writers Beware, which focuses on alerts and scams (hugely important for newcomers!). It also touches on major current issues in the publishing industry - you can branch out from there into other blogs and resources.
Be Good; Be Lucky; Above All - Be Persistent
There's no guarantee of anything. If you're good, and persistent, then you can almost certainly break in somewhere and in some way. Probably no way to predict right now when and how that might be. If you're not good, and you are persistent, you can practice and get good. Either way, you'll have a LOT of hard work and frustration on the way.
That's why the goals are so important - a lot of them you can reach regularly, as you go. If you're waiting all the time for that first acceptance letter, you're probably going to be waiting a long time, and you might not make it that far. If you've got drive and satisfaction to keep you going - well, again, no guarantee, but your odds become a whole lot better.