[limedaring]

First, smaller is easier for meeting people and actually have worthwhile conversations (jumping into a large group of well-known people at a conference afterparty isn't going to create any new friends, normally).

Find any local meetups first and go there. I went to my first networking conference, SXSW a few years ago, and met one person, who intro-ed me to three others. Contact continued when we were all on the same flight home, and I offered to drive them from the airport. These three then intro-ed me to new people, who then intro-ed me to more... this is the best way, imho, to create honest connections that don't disappear once you leave a party.

Also, Twitter is a pretty easy way to continue connections after you've met someone briefly.

As for approaching people to initiate conversations, just do it. Jump in, say hi, start listening, and speak up when you have the chance. But if you want to actually add someone to your "network", find a way to follow up after so they remember who you are.

[GeneralMaximus]

I'll add something to this: tag along with a friend who knows a few people at whatever meetup you're attending.

[limedaring]

Definitely helps, though it sucks to be in situations where you don't know anyone but still got to go meet people!

Also, coming with friends can have a downside, where you don't spend any time meeting anyone new. I will often split up from whomever I arrived with to meet new people on my own — sometimes it's better to do it apart.