First, ask yourself why you want to start a webzine. There are lots of good reasons, but if you can't give yourself a cogent answer, you might need to do some re-thinking. Webzines are easier to produce and maintain than print publications -- but they do take work. A lot of work, and a lot of time. I've seen a lot of webzines get started on the basis of the publisher's nebulous idea of simply wanting to do one; they seldom make it past the first issue or two.
Next, ask yourself what unoccupied niche your publication will fill. There are a lot of publications, both online and off. How will yours be better or different than what's already out there? These are important questions, because new webzines are very hard to promote, and you won't get readers if you don't offer something worthwhile and different.
Study your favorite webzines. Figure out how they work, and what you like best about them. Then use that information when you design your site. And, once your site is running, check your competition regularly to see what they're doing.
In design, a clean, simpler look is often better; the site should be about the text, right? Don't make more work for yourself than you have to; if you don't have a knack for site design, enlist the help of an acquaintance who does. When you're making a prototype page design, check it on as many different platforms and browsers as you can to make sure it looks good. If your Java-ridden site crashes someone's browser or is unreadable on a Macintosh -- you've just lost a reader. Get the best graphics and artwork you can. While the writing makes the magazine, people make their initial judgments on the aesthetics of the site -- they won't bother to read it if the art looks bad or if it's hard to navigate or the text is hard to read.
Figure out if you're going to pay writers and artists or simply "pay in exposure". You'll get better material and your publication will have better status in the eyes of readers and writers alike if you pay professional rates. But if you offer pay, even a modest amount, you're going to be inundated with materials, the vast majority of which will be unpublishable. I've seen publications die when their editors burned out from trying to read the tons of submissions they got when they started offering writers payment. If you get a listing in any of the Writers' Digest books ... brace yourself.
If you don't pay your contributors, don't even give the impression that you as the publisher are making money off the site. Some people will get extremely irate if you do, and you can expect hate mail. This means that if you don't pay, you shouldn't be selling ads and such on your site, even if you're using the money to pay for stuff like server space (if you have a worthy publication, you can probably find an ISP to donate space if you find the pop-ups and traffic limitations of freebie servers like Geocities to be irksome).
Figure out whether your webzine will run as a commercial or noncommercial publication. If you decide to go with the commercial option, your best bet is to find a corporate sugardaddy, like Chiaroscuro (www.chizine.com) found in Leisure Books. I've never seen a fiction/poetry webzine run successfully on banner ad revenues and subscriptions; other webzines that offer compelling nonfiction information (like stock market advice) or porn have managed this feat, though. If you go the noncommercial route, it may be worth your time to try to get set up as a nonprofit organization (this is what we're in the process of doing at Strange Horizons). As a nonprofit, you'll be able to get grants and donations. Strange Horizons has already done well enough in obtaining donations that we can pay professional rates to contributors, although all of us on staff are strictly volunteers.
The quality of the writing in your magazine will make or break it ... look for the best you can get, and treat your writers well. If you pay, pay them on time (preferably on acceptance rather than on publication), and respond to their concerns promptly.
If you're not personally overseeing the finances, make damned sure you know where the money's coming from and where it's going. Keep the best records you can, because if you're operating your webzine at a loss, you can potentially write it off as a business expense.
Your staff is crucial to your success. You can run a simple site essentially by yourself, but for anything the least bit complex, you need the help of at least a few other competent, committed people to help you. In dealing with a staff, especially a staff of volunteers, frequent communication is critical (weekly progress reports are good); try to keep people feeling involved and enthusiastic.
Make sure your stories and articles are cleanly laid-out and free of typos and code-os. Even if you are an amateur, you don't want to look like one, do you?
And finally ... trust your instincts, and follow them. Make good on your promises to your contributors, your readers, and yourself.
For more advice on starting a webzine, visit: