I am happy to hear that you are getting out there and networking! It is really awkward at first, but once you realize that everyone is there for the same reason (i.e., to learn and network), you will feel more comfortable.
It is important that you try to get to know individuals. Take time to learn about their background and once you find out which company they work for, make sure to try to get an idea of the culture.
I personally prefer to get the other persons information. Make sure that you ask them if they mind if you connect with them on linked in. To me, it is just a little weird for someone without a job to have business cards (I am in this group too! lol). It may appear to be too presumptuous. When you get home or the next day, send them a nice note through LI that let them know how much you enjoyed talking to them.
*If they tell you they will take your resume, don't jump right on the opportunity. I found that about a week later (after you have connected with them on LI or at least sent an email to thank them) asking them if they could speak to you by phone or meet you for coffee if looked upon much more favorably. Then, after that meeting if they offer again, go for it. Or somewhere towards the end you can ask if they would introduce you to the recruiter of the company. BTW, by this time you better have several reasons why you want to join the company! lol
These events are truly to meet people in the field and hopefully build long-lasting relationships. Don't bring resumes, just bring your best attitude. Dress nice. Think of a few points that you would like to make about you as a person. Many times, experienced professionals like to hear about new professionals' career ambitions. If you haven't 100% pin-pointed your career path, you might want to consider some questions that you can ask more experienced people about the field or getting into the field.
If this even turns out to be less of a networking sort of deal and more of a CPE type of event, look for events geared towards students. I know you are not a student, but you are entry-level, right? The last event I went to was a scholarship night. There were people there who were at all different stages in their career.
Please let me know if I can clearify anything or if you have more questions. I check in here a few times a day when I need a break!
Almost always from my phone... please excuse my typos!
All 4 passed - 2016
CA CPA