I have moved a lot during my career (Oz/China/Thailand/Europe/US, 8+ cities, now 35) and frequently that meant arriving in a new country or city with zero friends, family or support network and making do, so consider myself well schooled in this problem.

The de-facto approach is drinking. Drinking is a great way to meet people but it is often skewed toward young to middle aged people without family so can get old/tired/irritating/self-destructive. The good thing is it's easily available all the time and there's a ton of venues, so if you don't like one just browse for another.

As others have said there is no substitute for social groups... there are many options here. One good one is dancing, there are quite a few cool social dance groups in many cities now, swing/salsa/tango/etc, and in general talent is firmly not required! The younger me would have said it's not my thing, but now that I'm in my mid 30s (and married with kid) I think it's an awesome scene and regret never getting in to it! Seriously, check this stuff out.

There are also a few good team water sports with big social elements .. things like sailing, rowing, outrigging, dragon boating. Sailing is good because you can do the social side but also get some self time, while being part of a wider community. If you want more team stuff, you can sail larger vessels where it's total commitment. The other options (paddling style) are pretty full on social and may be a bit much, depending on your personality.