I've gone into this in the past, but basically, I think short stories could be revived using an iTunes approach. The writer sells directly to the reader, or through a short story site, for a low, low price. Say $0.25. If a thousand people buy your story, that's $250. Not a fortune, but it is something.
But that sort of approach is not ready for prime time yet, because online micro-payments has not really hit the mainstream yet. People have to have Paypal, or use their credit card currently, and while most people would be okay with linking these up with Apple, most people may not feel comfortable or be willing to do so for a tiny short story site.
Right now, I think the only viable model is to a) build a readership by giving it away, and aggressively marketing what you offer, and b) using an established reader base (as newspapers and magazines use circulation figures) to sell sponsorship. Not ads, but sponsorships, and this is an important point.
Looking at the state of short fiction these days, the declining readership may appear to signal a waning of interest in the form of short fiction, but the truth is that the interest is there so long as the delivery medium is convenient. Which is where podcasts come in.
A lot of magazines and newspapers have been including podcasts with other content online. The New Yorker even produces a fiction podcast. But a magazine like the New Yorker has deep pockets, and this sort of production would be peanuts to them.
One short story magazine that started from nothing and grew is "Escape Pod," with 209 episodes (issues) thus far. It's a Science Fiction Audio Magazine. If you want to check out an episode, a good example is Episode 158, both because the story is fun, and the episode is sponsored by the musician Jonathan Coulton. His song "The Future Soon" (an excellent track) is at the end of the podcast.
An interesting side note...lyrics from that song inspired the Cory Doctorow short story "The Things that Make Me Weak and Strange Get Engineered Away."
Escape Pod pays contributors about $100 a story, and $20 for flash fiction. Not a grand sum, but it makes them a legitimate publisher, and allows them to legally secure rights (nonexclusive rights) to the stories they buy. Since their launch a few years ago, they have become one of the largest markets for short science fiction on the web.
Even Garrison Keillor's "News from Lake Wobegon" podcast is sponsored. Usually by Cheerios. You can find that podcast on iTunes
The reason I feel sponsorship is the way to go is because you can sell exclusivity. The problem with selling "ads" is that you end up having to sell as many as possible, crowding them in the smallest space possible to maximize revenue. It worked great for magazines until it didn't anymore. For audio magazines, nobody is going to listen to ten minutes of commercials, free podcast or not. But a sponsorship is perfect for the form, because podcasts are a recreation of the theatre of the mind of the old days of radio. It is a very intimate and engaging experience, and in that format, sponsorships are much more effective because the announcer incorporates the sponsors message smoothly into the episode.
I know the whole money issue seems a mere piffle, a distraction from the real business of literature and good writing, but it is what allows the literature and good writing the opportunity to find an audience.
The idea is to use the revenue stream generated through the podcast sponsorships to pay for everything else. On the site you can post the story text, put a link to the audio version, and you can even carry over the sponsorship if you want, or not if you prefer the make the site look as un-commercial as possible.
Starting from scratch, however, unless you want to end up broke after 11 issues and unable to continue, like Farrago's Wainscot, which was a pretty cool online experimental fiction magazine, there has to be some way of generating a revenue stream.
Of course you could just do a free thing, and offer no payment to authors (which means you probably couldn't secure rights to their story), and hope word of the site spreads like wildfire. Unfortunately you would then face the problem of how to attract quality writing, and how to get taken seriously.