as a non-profit. If you think your idea fits the bill, then I don't think the paperwork required is very difficult.
From there, though, you'd have to start from scratch. Building a base of support is not easily done - it can be done, but I wouldn't count on grants to come flying in over the transom. Especially right now, both individual donors and foundations (not to mention corporations) are tending to support fewer charities, and those are usually charities they've known and supported for years already. Again, not saying you can't succeed, just that this is going to be a particularly tough climate in which to do it.
You're going to need to get up to speed on public relations, on grantwriting (lots of resources out there for that) and on generally how to talk about what you're doing, and why it will benefit people - and how, exactly.
If you're in this for mostly altruistic reasons, and you feel confident of your ability to tell that story in a compelling way, then go for it. Let me also warn you though - this isn't likely to be something that earns you a significant living. You'd be in it for what you can offer, not for what it can offer you, you know?
ETA: this is an IRS link - should have the basics of applying, I think:
http://www.irs.gov/charities/article/0,,id=96109,00.html