Attending an economics seminar is not a passive endeavor. It took me two years of attending seminars to start to get the hang of how to attend seminars. Here are a few tips, especially for new grad students. The first two tips are "necessary but not sufficient." The third is the golden rule. The rest are more practical, with a few just for women at the end.
(1) Know your stuff.
Obviously, if you want to be good at attending economics seminars, you should want to be good at economics. Prioritize classes and learning, in your first year especially. For newer grad students, you don't have to know all the fanciest models to contribute at a seminar. Understand the basics really well. Identification, endogeneity, robustness--these are some of the crucial things that need to be discussed at seminars, and you learn about them right from the start, so learn them well. After first year, learn your fields well. This includes learning the main themes, the seminal papers, the important open questions.
(2) Know you know your stuff.
If you followed tip number 1, you are qualified to be an active participant in the seminar. Other members of the audience know more than you, but don't be intimidated to make a comment or question when you know what you're talking about. But know that the speaker knows their stuff too, especially on their own research topic, so phrase things in a way that sounds polite, suggestive, confident but not over-confident.
Here is the golden rule:
(3) Speak for the right reasons.
This probably requires that you be in academia for the right reasons. Remember that admissions essay you wrote about how you want to study economics so you can prove how smart you are and gain power and admiration? No, of course you don't, because you wrote about how you want to contribute to the state of knowledge and improve our understanding of the world for the benefit of society. Keep that in mind. You do not go into a seminar to impress people. You go into the seminar to learn and to be part of the collaborative process that is academic research. Don't try to find flaws, try to find improvements. And if you do want to impress people, it is more impressive (both to the speaker and to the rest of the audience) to give someone a suggestion that can improve their paper than to point out how flawed their paper is.
Now for the practical tips!
(4) Sit where you can see and be seen.
You're all ready to be an active participant. So why are you in the very back row? Sit where you can see and hear what is going on. Sit where you can get the speaker's eye if you have something to say. Sit near someone that is good at attending seminars, maybe an older student you really admire. That can help you stay more focused. Also, introduce yourself to the person sitting next to you if you don't know them. Name, department, year.
Since you will be seen, look presentable. We're not in business school, and I know we don't have tons of time to play dress up, but putting on slacks and a decent shirt doesn't take longer than old jeans and a t-shirt. When I started grad school I was 21, and in jeans and a tshirt looked 17. It's hard to get called on if you look like you got lost on your way to high school.
(5) Don't try to multitask, not even a little.
Sitting where you can be seen will also make you less tempted to multitask. You won't get half as much out of a seminar if you try to do anything else at the same time. First year, whenever I tried to do problem sets or skim class notes during seminars, I didn't follow along well at all. Even checking email or something mindless will keep you from being focused enough to be an active participant. Don't have an ipad or phone out, and definitely not a laptop. If you feel the need to multitask because you are so busy, then you probably should not go to that seminar. If, on the other hand, you want to multitask because the seminar is boring, you should pay even more attention to the seminar and ask yourself: What is or could be interesting about this research? If you really pay full attention and keep thinking about that, you will likely not be bored and will likely have interesting ideas and expand your horizons.
(6) Use appropriate timing.
Don't raise your hand or shout something out whenever an idea strikes you. If you have a question or comment directly related to a particular slide, try to raise your hand near the end of the slide. If you think of something related to a few slides back, or something either really specific or really general that is not directly relevant to the current slide, wait until the end of the presentation. If the speaker is getting pressed for time and is trying to speed up, be respectful of that and don't raise your hand unless it's really important.
(7) Attend more seminars.
It takes practice! They will get less stressful and more enjoyable. Don't just attend the crowded seminars with well-known speakers. Plus, you will start to get to know the other "regulars."
Tips especially for women:
(8) Bring layers.
A lot of women tend to get colder than men. The room will be mostly men, who will keep the windows open even when it is freezing outside. The temperature in Evans Hall, and likely in many public universities, is a highly volatile stochastic process harder to forecast than the stock market. Prepare for multiple contingencies. You may get too cold to think straight unless you bring a sweater or two. Hang a sweater over the back of your chair so you don't have to dig around through your bag disruptively in the middle of the presentation.
(9) Attend other women's seminars.
Make a special effort to attend seminars with female speakers. At the macro seminar, I am sometimes the only woman in the audience. If a woman is going to present, I don't want her to have to face a room entirely full of men. Sorry men, I just don't. Plus, women tend to have slightly different presentation styles than men, and it can be useful to see what works and what doesn't. You might learn some lessons for when you give a seminar.