Don't expect to get that much out of a conference. Small gatherings can be spoiled by the usual suspects who tend to confound conferences with holidays, while the attendants of big conferences can often be too busy to chat. Consider to arrange meetings beforehand.

Don't miss the conference dinner, it's usually the best opportunity to get to know someone quickly. Choose your seat wisely, though.

Don't feel disheartened if you're participating in a conference in your field for the first time and feel a bit left out. Establishing acquaintances takes time, obviously.

A couple of things from my own experience:

More likely than not, there will be a person attending your presentation who will be hostile in the sense of trying to find something to criticize in order to appear as more informed etc., etc. Sometimes you'll get useful feedback out of that, sometimes it'll be good practice in defending your project, and sometimes it'll be stupid.

Shamelessly talk to people whose topics are interesting. I made some great friends at conferences and offensive friend-making is a useful skill.

If you are presenting for the first time, aim for the time they gave you (most often between 15 and 20 min.) Nothing is worse than someone going on forever.

Learn to recognize which spots are best. First one in the morning and the one after is good. Directly after lunch is bad because people will be tired. The mid-afternoon spot can also be good and the last one of the day can also see a drop in attendance.

Very important: If you have a presentation, videos or pictures send them to the organizers beforehand so that they can test if they run. I once was at a panel about the visual history of Nazism and someone tried to play a movie and it didn't work. Presentation gone to hell and it also seems unprofessional.

Sometimes conferences make you pay for attending. Think hard about if you really want to do that if you have no institution financing your trip. It can pay off but at the same time it can set you back a lot of money.

Be prepared. Unless you are the most gifted speaker out there, people will notice if you slapped you paper together the night before. I did that once and it was an unmitigated disaster. I also know a professor who thinks he can do that but everybody thinks he gives shit talks at conferences. So be prepared and if you are not the biggest fan of public speaking, practice beforehand with a friend or two or even in front of the mirror.

If you have a presentation (and I'd recommend you have one), use pictures instead of walls of text. Having some illustrating effect, can be very useful in breaking the monotony of some panels at some conferences and it makes one stand out.

If you are presenting for the first time, get a friend to write down the questions asked, who asked them, and your response. Speaking from experience your brain will be frazzled on adrenaline afterwards, especially if you go straight to celebratory drinks!

• Try out smaller, regional conferences instead of big ones. Not only are they cheaper (lower fees, often can skip the plane ticket and drive/bus/train there) you have more chance of having decent conversations in a smaller crowd. You also have more chance of running into friends, fellow graduates, past coworkers, which is the best part of conferencing.
• Dress for Success. Sensible shoes. Any woman who wears heels at a conference I look askance at. Don't dress up past what you would wear to work unless you are presenting or interviewing, you'll look like a dweeb. Nice Jeans are totally done now. But dress fashionably, distinguished. The Ritual Exchange of Compliments is the #1 easiest icebreaker for two women. Or two men, if they are of modern sensibility. Cross-gender compliments I cannot advise on. And do your hair and makeup nice. I suppose if you're one of those people who hopes to visit a few other hotel rooms at a conference, do your hair and makeup extra nice.
• A lot happens on the backchannel. It's usually twitter, though I'm starting to see slack groups form. Know the official hashtags. Know the secret hashtags. But keep it professional. Important People are reading.
• Presenters love when you livetweet them, use the official session numbers if you can, usually it's like #s504 or something, and try to tag them if you can find their handle. So you can get one guaranteed new friend out of this! I also use livetweeting basically as note-taking.
• The real conversations happen in the breaks and the dinners and the bars. Gossip, who's hiring, scuttlebutt. Up to you if you want to seek these out. But the most important stuff I've learned at conferences have been outside of the presentations.

edit: forgot my best tip!

• For Poor Students or those Otherwise Not Ashamed Of Economy: Those single-serving oatmeal cups make great breakfasts at a conference, because you can make them with the hot water from the in-room coffee machine, and then you don't have to go out for breakfast at Dunkin Donuts or something.

As someone whose job is not in the humanities, I'd like to point out that the many fine suggestions in this thread apply equally well to many other fields in academia including the natural and social sciences.

My experience has been that the networking opportunities at conferences is often equally valuable as the scholarship.

Don't be afraid to ask questions. As in any class, for any question you have in mind, there are probably four people thinking it who won't actually ask.

If something is interesting, make notes. Otherwise you'll remember three things from a day that had three hundred interesting details.

The ideal outcome of a conference isn't knowledge, it's inspiration. And possibly contacts, but mostly inspiration.

(I'm moderating a session at the Leeds Medieval Congress in July. It's not my first time speaking at a conference, but first time moderating. I'm looking forward to it immensely.)