I am contacted quite frequently by aspiring writers seeking advice on breaking into the publishing world, which is always amusing as I would love to break into the publishing world myself. But I have published some articles and I have an agent shopping my book-length efforts, so making the mistake that I know some stuff is understandable.
Plus, I do actually know some stuff. So there's that.

My wife also quite frequently receives copies of self-published books in the mail from aspiring authors who believe she has some pull in the Christian industry. The truth is, she kinda-sorta does, but not in the area of getting stuff published. (If she did, don't you think I'd be on the bookshelves by now?) But that doesn't stop people sending her their Xulon-printed paperbacks and half-cocked proposals.

As far as I can tell, there are two things every aspiring author must have (and a third that would be extremely helpful) to get even considered for publication:

1) Talent
You have to write well. I won't belabor this point, but most aspiring authors think they are good writers, and most are not. Some are passable, but only a minority are publication-worthy. Most bad writers don't know they're bad writers, and this self-delusion is really a turnoff.
But if you happen to have the self-awareness that you're not all that great, don't despair. The encouraging thing is that plenty of bad writers get published, which proves you don't need to have that much talent.
If you're a writer, keep writing. Don't trust your Aunt Mabel's assurances that you are good. Study craft. Keep writing; get better.

2) Education
I'm not talking about formal education. I'm talking about knowing how to work the process. Do you know how to format a book or article for submission? Do you know which publishers take unsolicited manuscripts (very few these days), which require agented submissions (more and more these days), which require a query letter? Do you know what a query letter is or how to write one?
Are you printing your cover letter on floral stationery? (Don't do that.)
Are you sending your self-published paperback to your writer relative who might know somebody who might know somebody in the industry? (Don't do that.)

Here are two fabulous places to start:

Nelson's Michael Hyatt on Advice to First-Time Authors

Mark Bertrand on formatting manuscript submissions.

You'll want to get the latest edition of the Writer's Market Guide to whatever it is you're trying to write, and it'll be helpful if you regularly read the blogs of editors and agents in the industry.
Conferences and manuscript submission services have worked for some people, also, but I don't think they're necessary.

Writing well and being informed, in tandem, greatly improve your odds of getting published. If you don't write all that well, being informed is especially important. A bad writer with an incoherent proposal or a query letter printed in 18-point Verdana will get nowhere.

This is the part where the "Self publish!" brigade rolls in to trumpet the praises of building demand by providing the supply oneself. It doesn't work. Doesn't. Sorry. Agents and publishers do not take self-published works seriously, because any joe with some dough can self-publish his book. The exceptions only prove the rule.
For every grassroots success like The Shack or that kid who ripped off The Lord of the Rings, there are literally hundreds of thousands of awful writers printing up their mediocre material and taking out pathetic ads to promote it.

Self-publish if it will make you feel better, if it will make you feel like a "real" author. Or if you already have a platform for speaking (or some such thing) that allows you to sell your books directly and regularly enough to make a profit. If you want to be published in the real world, however, self-publishing only makes you look like an amateur, and as there's no serious editorial filter, most agents and editors won't waste time weeding through the thousands of awful books to find the gems. Go through the prescribed process.

There is a hypothetical third way in:

3) Be "somebody" or know somebody
Plenty of bad writers who know nothing initially about the publishing process get published because they are popular preachers, notable politicians, or recognizable entertainers. Or because they know somebody with real influence in the industry.

I can tell you right now what most agents and editors are really looking for, though:
A very talented writer who is informed on the publishing process and also happens to be a recognizable figure in whatever field he's writing for.

Your mileage may vary.