For anyone in the UK, the National Autistic Society is a pretty good place to start:
http://www.nas.org.uk
Their website is extensive, informative, brilliant, useful... and abysmally difficult to find things on. This obscure link may take you straight to the right place, if you're lucky:
http://www.nas.org.uk/nas/jsp/polopoly.jsp?d=2176
At the top of the page it says:
Home> NAS services and support> Social groups
Unfortunately, the sidebar doesn't show that. D'oh!
Also, searching for "Social groups" doesn't get there.
I got there by knowing that I was looking for "Social groups", which is listed in their "site map".
Anyway... the NAS are pretty good in both running groups and pointing you at independent groups. Just email someone in the organisation - preferably choosing someone in your general region.
Since finding out about AS, back in 2006, I've been going to the NAS Yeovil group. Meetings vary around ten or so aspies, with a couple of parents or others acting as facilitators and an NAS employee as the organiser.
I've also met rather a lot of aspies, one way or another (e.g. here, work, and recently, Autscape). The more I meet, the more I learn about myself.
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"Striking up conversations with strangers is an autistic person's version of extreme sports."
Kamran Nazeer