The answer is simple: You make money by selling ads. I don't see how "the ephemerality of its messages and its young target demographic" would be an impediment to that business plan. Advertisements are also ephemeral, and teenagers buy things. But let's do some back-of-the-envelope calculations on that $3 billion figure.
Snapchat recently revealed that it serves about 350 million "snaps" per day. For comparison, in its IPO filing, Twitter revealed that it served 287 billion timeline views in the first half of 2013. During that same six-month period, Twitter made $253 million in revenue. So Twitter makes a little under a 10th of a penny per "timeline view."
If Snapchat generated as much ad revenue for each "snap" as Twitter generates for each "timeline view," the company's revenues would be around $100 million a year. Given that Snapchat still has a lot of growth potential, that $3 billion number suddenly doesn't look so crazy.
And a 10th of a penny per pageview is downright anemic as ad revenues goes. The New York Times generates around 17 million page views per day, or about 1.5 billion page views per quarter. And last quarter, the Times earned $32.9 million in digital ad revenue, which works out to about 2 cents per pageview. My experience as a freelance writer suggests that the per-impression revenues of other media organizations are similar.
The New York Times earns a lot more money per pageview than Twitter does, largely because Twitter isn't trying very hard to make money. The company has made a strategic decision to provide the best possible user experience, which it hopes will accelerate the growth of its user base at the cost of lower short-term revenue. Ads can be annoying, so Twitter has rolled them out cautiously.
But at any time, Twitter could slather its site in banner ads and massively boost its revenue. In fact, that's exactly what Facebook has done over the past couple years, with great results for their bottom line.
So Snapchat doesn't have zero revenue because it's impossible to transform 350 million daily snaps into millions of dollars of revenue. Quite the opposite. Snapchat is focusing all of its efforts on maximizing the size of its audience precisely because turning eyeballs into dollars is a solved problem.
The same point applies to startups more generally — including Twitter itself. People express amazement that a company that's still losing money could be worth $20 billion. That high valuation isn't proof that the market is crazy. It reflects the market's understanding that Twitter could be generating a lot more revenue if it wanted to. Tech startups like Twitter and Snapchat are confident that if they attract a lot of users, they won't have any trouble generating large revenues. And as companies like Facebook and Google have demonstrated, they're usually right.