That being said, there are ways to ask for art, and ways not to. Unlike some places, we'll never yell at you for not asking correctly, but there are still some things you can do (and avoid doing) to make your request more likely to be filled. I'd like to go over these today.
Be specific about what you want.
By far the biggest challenge in making art for FOSS games is that projects will have artists come and go, and because of that it's difficult to maintain consistency between pieces of art. It's possible to have a bunch of art elements that are all individually excellent but have a game that looks horrible because the art elements don't go together well.
The first thing you need to know is what general theme you're looking for. Describe it and provide examples and references. That will give your artists a general idea of what to go for.
If at all possible, you'll also want to provide a color palette for the artists to use. Your palette doesn't need to be enforced with an iron fist, but it does need to be enough to give artists direction so that whatever thematic elements they make will fit into your game. If you're making a game with a dreamy pastel theme, dark, gritty colors aren't going to fit (and vice-versa).
Provide design guidelines. This is particularly important for your user interface icons. Tell us how thick you want the outlines to be. Tell us if you want things to be angular (and, if so, what angles), or rounded. Should we use gradients? Pixel art? Vector art? Digital painting? If possible, write up a short document describing how to produce the general look of what you're going for.
Now, that's a lot to think about, and it applies a lot more to large requests than small ones. If you're only asking for a couple of things, you can get away with a few general bullet points describing what you want. If you've got a large, ambitious project, your design guidelines really ought to be part of your design document.
People have expressed hesitation in the past about making these decisions because they'd rather leave them up to the artists. That's a valid concern, and we'd love to help. If you don't have a set of design guidelines, come talk to use on IRC (#opengameart on freenode) and we'll walk you through the process. We may even draw some up for you by request, as long as you're willing to take part in the process. :)
Make it easy.
Art is like code. It takes a lot of time and effort. If you're asking someone who doesn't have a vested interest in your project to spend their spare time making you something, you have to meet them half way. Make a list of the specific pieces of art that you want, and make sure that it's up to date. Many projects keep wiki pages that show their art assets. If you have such a wiki page, it's absolutely imperative that it be updated with the art that you already have, so artists know which things they ought to be working on.
Don't expect artists to poke through your code repository to figure out what you need versus what you already have. A lot of artists aren't familiar with version control systems (nor should they need to be). In general, it's not a good idea to ask an outside artist to do legwork that you're capable of doing yourself. Even if you find an artist who's willing to do that work for you, the hours they spend organizing your project's existing art will be hours not spent utilizing their artistic talents, which is a waste.
Hopefully I'm preaching to the choir here, but be understanding of the fact that a lot of artists don't code. Many of them don't use Linux. This doesn't mean they're dumb or that they lack talent -- they like to work in an environment where they're the most productive. Artists (and other people) will tend to gravitate to projects where people are polite and accepting
Mind you, it's perfectly reasonable to ask that your art assets be created with FOSS tools, but be aware that it's a trade-off -- on one hand, it's a badge of pride for your project to have a 100% FOSS workflow, but on the other hand you shrink the pool of available artists. If you're going this route, explain yourself politely, and many people will be willing to work with you on it.
If you're coming in with a very ambitious project (like an MMO) and requesting very specific resources, be prepared to produce several hours of real gameplay. This isn't a hard and fast rule -- we make exceptions from time to time, based on circumstances. If the art you're requesting is something that would be generally useful to a lot of projects, we'll be more likely to help you out, because we know the time won't be wasted even if you don't end up using it yourselves. With one exception, we've turned down art requests for MMO projects that don't yet have solid gameplay. This isn't out of spite -- we just have limited resources, and need to put those toward projects that are more likely to succeed.
If your project is one or two people with a concept for a great MMO, you're not ready for art assistance yet. Expand your team and build a game. If we have the necessary resources, we'll try and help you once you have something that runs with real gameplay (quests, etc).
On the opposite end of the spectrum, some projects are essentially finished (playable, with placeholder art), and come in with relatively small requests. These are the types of requests that we'll address first and with highest priority, because we know that the art will be used almost immediately. If you have a mostly finished project with programmer art (or art lifted from unlicensed sources), we'd love to help you! Come talk to us. :)
If you have a talented artist (or musician, sound effects person, etc), and you need some art that's outside of that person's comfort zone, find out if they'd be willing to help out another project in exchange for one of their artists helping your project. There's a lot of art talent out there in the FOSS community, but there's not quite enough to go around for every project. Trading art between projects is a great way to get your requests filled. If your game project has talents (art, coding, audio, writing, etc) that you'd be willing to trade for other art, note that in your request, and someone on another project might see it and be willing to help you out.
I think the anti-commercial sentiment in the FOSS community is starting to subside a bit, but it's still out there. Artists have to eat and pay rent too, and if you'd like good art for your project, sometimes the best thing to do is just spend money on it (particularly if OpenGameArt can't help you for whatever reason). There's nothing wrong with spending money on a Free project -- remember, it's free as in speech, not as in beer. If you believe in your project and have been willing to sink a lot of hours into it, you might want to consider sinking some funds into it too, if you have cash available. I've commissioned a lot of art myself and I have a good idea where to look and how much people generally pay for good art, so I'd be happy to talk to you if you have questions concerning doing your own art commissions.
If you're requesting art from OpenGameArt.org, be understanding of the fact that some resources are harder to provide than others. Pixel and vector art, and untextured, low-poly 3d models are relatively easy. Sound effects, music, and concept art are somewhat harder. High poly 3d work, particularly with textures, takes the most time. Given our limited resources, we'll be more likely to spend our time where we can be the most effective. You can always feel free to request anything, but be understanding of the fact that some requests are easier than others.
Art isn't easy, and as a community we're still figuring out how to integrate artists into the FOSS movement. I'm kind of rare in that I'm a good coder and a decent artist -- not great, but enough to have some understanding of the issues that artists and coders run into when trying to communicate. If you don't know how to make a request, come talk to us, or make a post in the OpenGameArt.org art requests forum. If we need more information, we'll ask for it. :)
Thanks for reading!
(BartK on irc.freenode.org -- again, you can find me in #opengameart).