I've done a number of independent projects, using a new artist just about with each one. There are several ways to find artists, but I'll focus on how I've gone about finding mine.
I have to start out by saying that I've been fortunate to have a good paying day job as a lieutenant colonel in the Air Force. That's helped me by providing me money to pay a small page rate to my creators, which means I've gotten more serious contenders. Although it's not what the Big Two at Marvel and DC can pay, at least it gives them a professional credit and it gets you much more talented individuals. Even if you can only pay a little, it will help immensely in finding more qualified comics creators. If you don't have funds to pay a page rate, you'll have to really find someone as hungry and dedicated as you to break in, and you'll have to convince them that you're the one that can help get them there, meaning you need a knock-out story that suits their artistic talents.
There are several sites out there that showcase artists (such as deviantArt), but I've used DigitalWebbing.com to find my artists. In some cases I've posted a want ad for pencilers, inkers, colorists, and letterers, and other times I've scanned the forums sections, in particular looking at both the Artist showcase and the Sequential Art Showcase. When scanning what people are posting, I check out their website, if they have one listed, and any other pictures they may have posted. I also see how their responses are with people, to get a sense of what their personality is like and what they might be like to work with.
I really work to find the right artist for the tone of the book. That's led to me using Alex Amezcua for a 1-issue pitch for science fiction adventure series The Rift, found here (it's based on a published short story I did a few years ago). I've worked with Jake Bilbao on a 4-issue horror series, Devolution, found here, and I was fortunate enough to get Jake his first work at Marvel on a Wolverine story we did together. I've also worked with William Allan Reyes on Redo, an independent superhero story, found here, and we're still shopping for a possible publishers for this. I've worked with artist John Amor on my series ClosetWorld, picked up by Arcana Comics (you can see more of his art here). And finally, I've worked with amazing artist Sedat Oezgen on The Chosen, found here, and we're developing a pitch together now for series A Heart for al Qaeda, along with co-writer Kevin Maurer. This doesn't count the numerous inkers, colorists, and letterers that I've worked with.
As a writer, I'm not competing with my artists to get work from the Big Two, and they know I'll go to bat for them any chance I get. I've stood in 2+ hour long lines, waiting to show the artwork of my artists at convention portfolio reviews. They know how dedicated I am on their behalf, and as a result, they've worked extremely hard for me, giving me some inspired work to share.
In each case I had a contract with my creators. This helps keep everyone clear on our respective responsibilities (such as when I have to pay them and when they have to have artwork complete after receiving a script). It really keeps everything professional.
Whether it's through a want ad, hitting someone up through a comics art site, or going to a convention and talking to artists in Artists Alley, there are several avenues to find good artists who are looking to break in. You just have to come up with a great story and concept, be easy to work with, and handle everything professionally (e.g., if you're paying a page rate, make sure you make payments on time for the full amount).
Good luck on finding just the right artist for your own project. Now don't go stealing mine.