How to overcome difficulties of social interaction at my first academic conference
I also went alone to my first conference, and did not know any of the other attendees beforehand - but I had read some of the works by some of them.
Besides the usual advice "talking to other that also look like they feel alone", I would also encourage you to
prepare and ask questions after talks.
Do this especially for smaller talks (if there are any). This really has many upsides: You practice formulating questions - a very important skill to get something out of a conference. You may get into a nice chat, which, in my case, turned into a friendship more often than I expected. As a consequence, you do not feel alone anymore.
If you did not get the chance to ask your question, you may also approach the speaker after the talk (either right after the talk but also in the next coffee break). Generally, scientists love to talk about their (published) work.
You'll be totally fine. It's perfectly appropriate to walk up to random people and say "hi! I don't think we've met - I'm so-and-so." Then just chat about what they work on, where they're based, etc.
Incidentally, one piece of advice I was given that I found really helpful: conferences are much more useful as a chance to meet other graduate students than they are as an opportunity to meet fancy big-shot faculty. Your graduate student contemporaries will be your community in the field, much more so than senior figures: these are the people who will be willing to read rough drafts of your work, give you a sense of where the frontiers in the field are, commiserate with you about your employment prospects, etc. And apart from anything else, it's typically easier and more fun to hang out with people who are at the same stage as you!
(This isn't to say you shouldn't talk to senior people if the opportunity arises, obviously. But don't sweat it: your main priority should be having fun and making friends.)
First of all - there's no silver bullet. I share some of your background - averse to parties, feeling the odd person out, slight anxiety - and after several "first time ever" conferences (I've switched academic fields), I can't say it has gotten that much better. I've just learned to sort of "buck up" and force myself to socialize anyway.
Some suggestions, though:
Try again after failures: You managed to somehow sit alone in a lunch break. You were going to talk to a speaker after a talk but other people got in the way. You didn't get up in time and missed seeing people at breakfast. Some of these things are going to happen. Don't sink into a dark mood and sulk in the corner! Try again in the next talk, next meal etc. And yet again after that.
Have an Elevator Pitch ready: Suppose you're standing at some table in some short break at the conference. Someone walks up to you and says: "Oh, you're from ABC University?" or "Oh, you're the guy/girl with that XYZ paper, right?" when you shyly reply "Yes, that's me" they ask you: "So, what do you do?" or "What are you working on?" - you need to have an answer ready. A 1-sentence answer is relatively easy, but if they're slightly more interested, you can't lay a 15-minute talk on them - the next session is coming up and they have other things to do, and are probably tired. So it needs to be something very succinct, somewhat exciting, that relates to what the rest of the community is doing ("relate" can mean "goes in a different direction"), that would be interesting or entertaining to recount to someone over a short period of time.
Not only is it important to have this in your head for actually recounting it, but the very fact that you can explain what you're about often helps you to relate to people and feel somewhat less awkward - as you can sort of justify your existence or your presence in the conference in another way than just suggesting people read your paper.
Stare at badges: One of the things that's always difficult for me is to read the small print on badges of people while they walk around. Even if it's embarassing to stare at someone's stomach, chest or a woman's breasts - they have a badge, so you stare. In fact, explicitly say "I'm trying to read your badge" to get them to stand still. By the way, this is a (weak) ice-breaker for a conversation.
Pimp your own badge: Create a second side copy of your badge in case it flips. Add a sticker you brought from home. Draw in something that has to do with your work (I put 'GPU guy' in a spiffy font). That's an excuse to draw attention to yourself in a non-conceited way - and also a good excuse for why you're staring at badges.
Ask people you don't know questions: Are you standing in front of someone you don't know, kind of up close and having caught their attention? This is an opportunity. Embarrassed that you don't know him/her? Say "This is my first conference" or "I'm new to the field" and then "Can I ask what the XYZ group at ABC University focuses on?" (assuming it's an XYZ conference and you've noticed from the badge that you're talking to someone from ABC University).
Remember: Everyone knows first-timers are fools who know nothing Actually, lots of people are fools who know very little even after coming the 10th time; and nobody really knows much about the sub-fields that they're not working on. So - even though it's a fancy-shmancy conference, it's ok to be ignorant, and you're not being an exception to the rule. No problem whatsoever if you say "I have not gotten into XYZ yet, but I still wanted to ask you..." or "I have not gotten into XYZ yet - since you're an expert, would you mind recommending a good starting point? Like a survey, or a few key papers?"
Explicitly trade off some of your time for social interaction When you're in a conference for the first time, you probably want to experience everything that's possible: Lots of talks seem exciting and useful; you want to make connections; you might want to explore the city you're in; you want to you want to take a lot of notes; you want to check out books and journal issues that are on sale; etc. This pressure to squeeze in everything makes it difficult to focus on social interaction. For example, you may be anxious about an upcoming talk that's about to start while you're striking up a conversation with someone. It's a bit of a challenge, psychologically, to tell yourself "I'm giving up on concretely and clearly useful conference activities in favor of informal chatting with people, which may or may not happen and may or may not lead to anyhing." - but you still need to do this. So you decide you will miss that talk but be more relaxed and have time to develop a conversation.
You can ask people to meet and talk later. A conference is busy and noisy; and people can butt in to your conversation. For many, this is a stressful setting in which to interact, especially when you're nervous about approaching some of these people, regardless of the environment. Well, it is very common and perfectly acceptable to ask people on "dates" - not romantic dates, talking dates: "I am working on XYZ, and I know that you are (etc. etc.); do you think you'll have time after today's schedule ends / tomorrow morning / at lunch break on Tuesday to sit down and talk for a while?" Note that conference venues often have cafes/restaurants close-by, and even if they costs money (as opposed to the conference, where you get freebies) - it's a very worthwhile investment. Plus you can sometime get reimbursement even for that.