Best way to build a social network in a new place?

Churches work great for this. If you don't believe in God then well, neither do many Unitarians.

Maybe this is obvious (or maybe it's a quirk of mine?), but I find the key to making friends is participating in activities that bring you together with the same people over and over. Going to meetups works if you commit to going several times to the same one; intramural sports leagues can work great; hiking or biking groups can be great; volunteering can work. But I think the key is repetition. Even if you don't immediately click with someone the first time, don't be discouraged right away, go again, at least 3-5 times. +1 for meetup.com, especially moving abroad you'll tend to find expat groups and language learning groups, and don't be shy about starting your own if meetups don't exist yet for your atypical activities. If you use Facebook I'd suggest posting something like "I'm moving to Blahville, does anyone have friends there they'd be willing to introduce me to?"

I know you said you know no one there, but does anyone you know have connections there? 2nd and 3rd degree connections - so and so's 2nd cousin, so and so's college roommate's other friend, and so on. Whatever your atypical interests are, can you find meetup groups or community organizations that are part of whatever this scene is? Email them ahead of time to find out about volunteer things you can do, get something on your calendar. Professional groups are good too - also on MeetUp.com, LinkedIn might be a place to look as well. Good luck!

Go out and do stuff when you get there. It really is that simple. Find meetups around your interests, volunteer for a cause that is important to you, get involved in your neighborhood, join a kickball team, whatever. Just do stuff where you are likely to meet people with the same interests as you. If you are moving to a decent sized city there are likely multiple opportunities every night to do stuff.

I took dance classes when I moved to Detroit. It helped that I already was hooked into the community where I lived previously. Dance will fulfill all of your needs and can be found anywhere. Whether it is salsa, tango, ball room, swing, etc you can find a community anywhere in the world.

I've had shockingly good results milking the social capital built into this very MetaFilter we call home. Is there any way you could do that without revealing in a post where specifically you're moving? This is more travel/expat based, but when traveling I've had good luck meeting people through couchsurfing.com. I've never actually "surfed" any couches, but they have meetups and activities listed on the site for cities all over the world. When I was in Turkey earlier this year and found that I was literally the only person staying in my hostel, and the owners spoke no English, I went to some couchsurfing sponsored English Language Exchange nights and met a bunch of cool locals who I could actually talk to. Even if you're moving domestically to a place where language skills aren't an issue, it's still a great way to get groups of people to do interesting things with. Which in my experience can be an issue if you're on your own but want to do something that's typically more fun in groups. The only thing is that they tend to have general meetups in bars, but assuming you don't have a terrible drinking problem you could definitely go along and just order a coke or something. In my experience they're not drunken free-for-alls.

Cyclists can be the friendliest people that often gather in bunches to go on rides. Search your new city to see if rides are happening, to see if there are bike spaces (not bike shops but places for people to gather to work on bikes, such as the Bicycle Kitchen in LA).

I have had good luck with meetup and so did my friends who moved to Stockholm recently. I always think volunteering is a good way to meet people.

Oh one other thing-- I think you are more likely to make friends if you are willing to take on a leadership role within a group.