I'm an artist who asked that same question some time ago. I can't speak for DUNGEON specifically (I've done cartography for DUNGEON but not illustration). Even so, I've had success with other companies, and here's what I've learned about the industry as a whole.
Editors are always looking for new artists, but standards are high. DUNGEON obviously contracts with some of the best illustrators in the industry, so their standards are likely extremely high. Editors in most gaming companies prefer to be approached with an email containing a link to the soliciting artist's website. That lets them review the artist's work when their need arises.
If you don't have a website, you can try attaching two or three of your very best images as jpegs to the email. This is not the favored approach, however. I tried it several years ago with several companies and heard back from DUNGEON and Fantasy Flight Games, but no one else. I got far more responses when I created a website and referred the editors to that. I fear cold-calling them with jpegs attached to emails smacks a bit of desperation. Perhaps professionals are expected to have websites.
If you're an adventure writer too, try submitting a single jpeg of a jaw-dropping image along with a query or manuscript submission to demonstrate the full range of your skills and talents.
After you submit your email, practice both patience and persistence. Wait at least a month or two before trying again, but try again! Needs change, editors change, and your own work will change, all of which are good reasons to try again.
If DUNGEON passes on your work, don't panic. Try other publishers. Go through both DRAGON and DUNGEON and make a list of their advertisers, many of whom are publishers. Go through each magazine's Gamer's Guide section too. Solicit work from these non-Paizo publishers, take projects, and build your resume. There are a boatload of collectible-trading-card-game publishers out there who need illustrators all the time. Many will try new artists.
When you do communicate with any editor, be concise, friendly, and enthusiastic. Show your love for their genre so they recognize a kindred soul. Don't try to be funny unless you really ARE funny (my frequent shortcoming). Use a proof-reader other than yourself. Be professional. They are, and they appreciate it in those with whom they work.
Good luck!
I would highly suggest a website. If you don't have one, you can get a space for free on deviantArt. If you do make a submission, I would include a friendly introduction with a link to your website.
Just my suggestions, as I haven't ever made an official Dragon/Dungeon art submission.
A few other places for artists to monitor:
http://www.enworld.org/forumdisplay.php?f=68
http://forum.rpg.net/forumdisplay.php?f=12
http://www.digitalwebbing.com/forums/forumdisplay.php?f=67