It's never been easier to raise money for your indie film or webseries. Today, producers and directors utilize a method called crowdfunding, which, according to Wikipedia, "describes the collective cooperation, attention and trust by people who network and pool their money and other resources together, usually via the Internet, to support efforts initiated by other people or organizations." In short, crowdfunding is how you can get your project financed -- in small increments by other folks.
Crowdfunding is sort of like microlending, in a sense. Individuals (either those you know or are related to, or total strangers) each donate small amounts of cash, ten bucks or so.
The most well-known websites for crowdfunding are kickstarter and indiegogo. But don't think you don't have to use at least a little bit of your own money to raise hype around your project. After all, we all know we need to invest money to make money. The indie films or webseries that are most successful at raising funds are those that have slick trailers and photos. Ultimately, the filmmakers have gone through some trouble to make something that is attractive so that you want to see more. Gene Massey of Cinema Shares, says it's pretty easy to see why the films that get funding via crowdfunding do so: "You'd look at that and say, 'I want to see that made.' " According to Massey, it's also pretty easy to see why the projects that didn't achieve their desired funds failed. These were the projects that didn't scream out to the viewer, "Hey, I need to be done."
But Massey also warns not to think that you don't have to give something in exchange to the people who are giving you money. Filmmakers can create different levels of incentive: donate $50 and you get a T-shirt. $1000 might get you an executive producer credit.
If you want to learn more about crowdfunding, check out a great interview on blogtalkradio, moderated by Gini Graham Scott with Gene Massey of Cinema Shares.