Take advantage of college and university resources. If you've attended college, you may be able to rely on your alma mater's career center for assistance (in some cases alums pay for counseling). Often local community colleges offer career transitions support to the public (call ahead to ask!).
Consider temping for a nonprofit. Larger nonprofits may rely on temporary employees ("temps") to fill short-term staffing gaps. Call the main number at a larger nonprofit you'd like to work for and find out which temp agencies they use — then sign up with those agencies. Make it clear that you are looking for nonprofit opportunities.
Use the internet to search for both job openings and organizations. Often organizations will post job openings on their own website first. Search nonprofit organizations on Idealist.org, Guidestar, and Charity Navigator.
Reach out through social media. Use blogs, Facebook pages and groups, and Twitter to meet people in your field. Often formal networking conventions (for example needing a friend to introduce you) aren't necessary in online social networking. Be professional and other networkers will notice your regular, thoughtful comments, questions, and retweets. Use search engines like Google blog search and Twitter search to find people who are working in careers you're interested in, too.