I moved to my teeny tiny village about 3 years ago. It is right smack bang on the edge of SmallTown, where the main shopping is. (we barely have a corner store here.)
POD to the other posters that suggested talking. Everyone here wants to stop and chat for a bit. I occasionally walk my two (small, cute and very friendly) dogs in town, everyone, and I mean everyone, wants to stop, pet the doggies and talk. So if you have the time, go for it. Cute toddlers are probably even more effective.
Patronise local shops, regularly. If there is somewhere local to dine, such as the local pub, go there to eat regularly.
Talk with your direct neighbours when you see them.
There's a surprisingly large number of local events on - trivia nights, plays, parades, car boot sales and markets. Go to those you can - they mightn't be big flashy events, but lots of low-key fun. There was a Christmas panto on here last year, it was an absolute riot of laughter, everyone had a wonderful time - big, small, old and young.
If the town is old, there's probably a historical society or something similar, if you're interested and have the time, get involved with that too.
When people know you're renovating the 'old Smith place', be prepared for a few who might be interested to come and see what you've done with it.
And understand that everyone knows or is related to everyone else. You'll find people know your name when you don't know their name, it's because you're the 'new kids on the block', so you'll stand out a bit for a while. I still get 'oh, you're new here, are you up at the xx place?'.
Good luck OP - I've found it's a wonderful change of pace, and I'm loving it.