1. Professional conferences have many versions. But the typical ones in Economics include three types of presentations: long presentation (18/20 minutes), short presentation (9/10 minutes), and poster. You will have to submit an abstract or a full paper. They may ask you if you have a preference for short presentations or long ones. If the paper is not selected for a full presentation, they may ask you if you want a poster. As a graduate student, I think you should take any chance to attend and present your work. However, be careful about your budget and reimbursement too.
2. I have attended ASSA conference just to see how big conferences work before I submitted to any conference by myself. It was expensive, but I think the whole experience helped me in the long run. It is a good investment. I also have attended the Heartland Environmental and Resource Economics conference at UIUC multiple times before my own conference presentation. I guess all these helped me to prepare. At the least, I knew what to expect. If you can manage time and money, I suggest you attend conferences before your own talk just to see the system.
3. Presentation: If you are an international student and if you are not coming from an English-medium school, there is a good chance that you feel awkward about saying almost anything. I believe that you can hide your nervousness by spending lots of hours in preparation. Know everything about your slides. Have a mock presentation. Make sure your slides do not have spelling errors. Make sure your slides are readable. Make sure you do not need to read from your slides. Make sure your slides are self-explanatory too. If your slides are perfect, and you are well-prepared, it will be harder for people to ignore your work.
4. Fashion: I definitely did not have any idea about professional clothing before my first conference. I asked around; some female professors and some senior female colleagues helped. The basics are pretty simple: a formal shirt, a formal pant, shoe, and maybe a blazer if you want. You can try informal dresses too if you are just attending (not as a presenter), but I think you will feel more confident if you are dressed like a professional. These things are expensive, try second-hand shops. You will get nice almost-new stuff.
5. Notebook: Do not forget the power of a pen and a small notebook. Always have a set with you. There are always ideas, questions, debate around you - you need to keep track. Laptop does not do the trick.
6. Business Cards: Some senior friends suggested that I get business cards. So, I actually had business cards with me in my first conference. I could not manage to give it to anyone though!
7. It is better to go to your first conference with some friends - fellow graduate students from your school. You will feel less awkward. You can share expenses, and you can attend talks together.
8. In those open bars, you may feel "nobody wants to talk to me". Actually, I have met some other graduate students from other schools in these conferences who were also feeling awkward, and they are very good friends now. So, try finding other people around your stage, they are going to be your colleagues for a very long time. It is OK if big people do not want to talk to you at this moment!
9. Sessions: There are normally lots of sessions. Try to attend some big picture sessions - like keynote, panel discussions. These sessions will help you to see where the field is going. Attend some method sessions to learn cutting-edge methods. Make a mixture of sessions to attend.
10. If you have any particular question to ask to anybody, you can definitely try to set up a coffee meeting. If you want suggestions from some specific experts, it is fine to invite them to listen to your talk. Know how to write cold emails.
11. Question-answer period: Normally, there are 2/3 minutes after every talk where you will get questions from the audience. Ask questions, engage in the discussion. I always find this helpful to learn. If you get a question that you do not know, it is OK to be honest. If you find the answer later, you can send an email to clarify.
12. Thank you emails: If somebody gave you a good suggestion, it is good to send a note after the conference.
Well, these are just some things that I learnt in the last five years. Hope this helps!
Finally, enjoy the conference experience. You will attend your first conference only once! :)