Career fairs are happening all the time, so check often to see if there are any happening in your area. You will have to choose the fair that has the most relevance to your search. This can be done by checking which companies will be attending. Most fairs will have this list on their websites, so you will be able to see if there are any nonprofits attending. Once you find that out, you need to start preparing.
Make sure that you bring enough copies of your resume and cover letter. You may only be planning on going to a few booths, but it's better to be over-prepared. You should also prepare a number of elevator speeches tailored towards each organization you visit. Remember to practice them enough so that you don't have to read off of a script, and don't be afraid to improvise.
When it comes time to head to the fair, try and get there at least an hour before it begins. The crowds will get larger as the day gets later, and you will find it hard to get everything done when you are competing with hundreds of other people. This also has another benefit: It will show potential employers that you are serious about creating good contacts. Make sure that, along with your resume and cover letter, you have a number of business cards that you can give to potential networking contacts.
The most important thing you can do to prepare for a career fair is to set goals. Aside from speaking to all of the organizations you are interested in, try and get X number of business cards by the end of the day, or some other tangible goal that will motivate you. It can never be overstated how much reaching a goal can boost your confidence and make you feel accomplished.