Do some research and choose your first destination(s). Do you want to try an internet startup in Asia? Work for an NGO in Central America? Backpack through Europe and pick up odd jobs on the way? A lot of people come to me and say, "I want to live abroad, how can I do it?" Well, it depends where you go. You can live like a king off $1,000 in Thailand or the Philippines, or spend that much in a week in Brazil. It depends where you're going and what you're doing.
The other factor is your financial obligations. If you have debt back home you need to factor that in. If you have health problems, then you need to do a lot of research on that as well. The good news is if you're an American, you're going to save a LOT of money on health care by leaving the country.
Calculate the amount you need to earn passively per month to survive wherever you want to go. This may involve getting a job once you're there. It may involve saving up a bunch of money now and selling stuff. It may involve creating passive streams online. Either way, budget it out so you know when you're ready.