There are some nonprofit job search engines (just search something like "nonprofit jobs"), but another way is to pick an issue you feel strongly about, and then do some web searching to find orgs that are working on that issue. Then check their job listings to see what they're looking for.

Nonprofits tend to not grow very fast, so there might not be a job that's exactly what you want to do. If you can find one or two orgs you like, you can get your foot in the door through volunteering first.

There is also a healthy ecosystem of companies that provide support to nonprofits. Nonprofits often outsource parts of their technology, so another way to get into the nonprofit world is through a digital agency. I would try looking for tech jobs in the DC area--a lot of the companies in DC that support nonprofits will happily hire remote developers, project managers, etc.

Check out http://www.idealist.org/