
Last Thursday, I decided to go to Ramit Sethi's book launch of I Will Teach You to Be Rich for three reasons:
I have been there before...I've been attending events in a totally new industry for me and had a rocky start. I ended making one contact who I would then send a note to beforehand "Hey there, I'll see you at Event on Friday, right? Wasn't there someone you wanted me to meet?" He almost always has many people already to introduce me to, and I've managed to get by.

At Ryan's suggestion, I attended a tweetup in my area, without knowing anyone. I'm normally a terribly shy person anyway, but I decided to give it a try. I went alone. I approached a group of people, found the person who was maybe a slight outlier, and just introduced myself. We got into the whole "what do you do" conversation, and just went from there. I enjoyed meeting new people and making connections.
I took my sister with me to the next one, and had an even better and easier time. It just takes a "hello" to get things moving.
Actually, for someone who's an introvert, who ends up emotionally drained by prolonged contact with people, and an Asperger who just can't decipher all the body language and the seemingly illogical nuances of social interaction, this is pretty typical of their experiences at networking events. For most of these events, I'd prefer stapling my head to the floor with white-hot dull staples. It ends up being less painful.
I'm an extrovert, and I've still struggled at networking events if I don't know anyone there. It can be really hard to walk up to someone and say "so, uh, are you part of the networking event?" and try to start a conversation from there.
I've found it helps if I know what I'm going there to do, and have my 2-line introduction at the ready. It can't just be "I'm going to go and meet people" it has to be "I'm trying to meet people who would be interested in hiring me as a writer" or "I'm here to advertise my new massage practice." Then when people ask, you know what to say.
Also, remember that everyone else is there to network, too. Chances are if you walk up to them and just ask if they're there for the event, they'll at least shake your hand and ask what you do. Then you can take it from there.
I'm right there with JRandom42. I'd rather be doing ANYTHING else rather than dealing with other people.
The only thing that has seemed to help me, is doing something else while meeting people. Going somewhere ONLY to meet people is excruciating to me. Instead I need to go somewhere to do something ELSE, and happen to meet people along the way. This takes the pressure off.
For example, I met my wife while playing pool at a bar. Now, I'm a very introverted guy. I didn't regularly date until I was about 25 (and I hope everyone realizes how difficult that is for me to admit). I found a neighborhood bar/club where I could go and order a pitcher of beer and play pool.
That was why I was there. To drink beer and play pool. I could talk to people at the bar, while I waited for my turn to play pool. I could meat women.... while I waited for my turn to play pool. I could make friends..... while I waited for my turn to play pool. I could wait for the perfect song to ask my future wife to dance... while I waited for my turn to play pool.
Having something else to do was my 'out'. Of no one wanted to talk to me, then I could always just go back to playing pool. Because, hey, I wasn’t there to pick up chicks... I was there to play pool. It made the possibility of rejection less painful, even though I didn't get rejected very often.
Soooo.. here is my point. If you find it hard to network with people, pretend you are there for something else. You are there to drink, or listen to the music, or play pool, or meeting someone else (good point Irina!).
Then you have an 'out' that will help you to approach someone else. If they are busy or aren't interested in you... well it doesn't matter, because they aren't why you are there!
Yeah, it's a mind game you play with yourself, but it worked for me.
I've been married for 14 years.

You aren't alone. My boss asked me to go to a "meet and greet" with one of our vendors and I was so intimidated (not to mention the only people there were male computer programmers who spent most of the time talking about sports) that I spent most of the event standing by the window eating cocktail shrimp (which was delicious!).
I managed to make a few connections with women I met on a trip to the restroom.
Personally, I always advocate bringing someone with you because at least you'll have one person to talk to when things get slow. I recommend bringing an extroverted person who will do most of the work for you.
I was once invited to a launch of a new product because I was interviewing for a position there. My seemingly simple request to bring a friend was denied. Awkward! The only people I managed to network with were those also applying for the job. It was horrific and I can't believe I survived.

This may be a dissenting scandalous opinion of mine, but I think having a friend at such events can be a double edged sword. Yes, it helps your confidence when you pretend that you are there to catch up with a friend--but then occasionally, you just end up feeding off of each other's anxiety. You stand there saying "Should we go talk to that person?" "Should we approach them?" And you give off a vibe that says "We are here to catch up, not to network with YOU."
Having a friend gives you a safe zone. Between chatting with a friend and approaching a new person, it is safer to chat with a friend. But when you are choosing between drinking by yourself at a bar and approaching a new person, the latter might be actually LESS awkward.
Of course all depends on the event and on the friend you are bringing. But if you want to start talking to random people, your best bet is....to start talking to random people.
I'm all about coffee and conversation. I think Ryan's idea is right on. Also, the more you think about it, the more you will over think it, so just say hello, and introduce yourself. I generally look for people who are expressive, who appear open to conversation, not someone who looks as uncomfortable as myself.
Everyone, thanks for all your great comments! I wrote this post with the intention of generating a conversation about how awkward and hard networking can be for anyone and I'm happy to hear that people share in my thoughts. Also, this shows that everyone is in the same boat at these events, so we shouldn't be afraid to approach other people.
@ JRandom42 - it's funny that you say that, since I consider myself an extrovert and so would most people. I think I am just overly sensitive to situations where people feel uncomfortable (=awkward).
@ Tatyana - this is true...unless both people come with the intention of networking and help each other out, push each other on. I think my friend and I were just too tired to keep doing it.
@ Jason Simon - your advice is right on and I usually do this. But that time was such an epic failure that I decided it merited its own blog post I really dropped the ball on that one. :-)