I just posted about the nonprofit career event at Notre Dame, so this is an ideal time to talk about some of the things you will need to do to make sure you shine brightly if you decide to go to it (or any event like it, for that matter).
For one thing, you should bring copies of your resume. As for which resume you bring, that will be a tricky question, as you obviously aren't going to know the representatives from the various nonprofits that might be there (though if this is a career fair, you might have a better idea of that). If I were to make a recommendation, however, I would bring the resume you base all your various revisions off of. You should give these to any nonprofit employees you talk to.
When you start your networking, you should almost treat it like a less formal interview. What I mean by this is that both networking and nonprofit job interviews have the following thing in common: they both give the employee the chance to get to know who you are and what your skills are. Really, the only real difference between networking and job interviews is that you aren't necessarily going to be talking about a specific position, and it is a bit more conversational than a job interview.
If anything, networking events can be a little more stressful than job interviews. You are going to not only be surrounded by many nonprofit reps, but many other individuals just like you; people wanting to break into the non profit sector. It's going to be hard not to feel a little competitive. I remember at my first networking event, I felt like I had to out-do everybody; this is the worst thing you can do. You should definitely do your best to impress, but not at the expense of acting like someone you are not. All this will do is add extra stress and make you come off poorly. Trust me, if you want to get a nonprofit job, you are going to want to be genuine.
So what should you talk about at a nonprofit networking event? Well, it's really up to you, but you should certainly mention (if applicable) any nonprofit work you have done. You should also mention what your previous job was and what about it lead you to pursue a nonprofit career. But perhaps the most important thing you can do is get as much information from the representative you are talking to. Does he/she know anybody you know in the industry? Are there any job openings at their organization? Any type of connection you get from this person will be extremely helpful to your job search.
Finally, talk to as many people as you can. It's natural to feel a little exhausted after a few conversations but remember, you are at this event for your nonprofit career. And there is no such thing as having enough connections, especially in the nonprofit world.