Good question! Good because it's hard to answer, but important and interesting. If you have any interest in mathematics, you could study a niche field in which case you'll meet pretty much everyone researching it. You could also read a lot of papers and try publishing your own or start a blog discussing them. If there's a book club in your area, maybe you could join it and meet people there? The easiest way though might be if your job or hobby has led you to some questions you'd like help answering, in which case you might send off an email to somebody who has a similar passion that can help you solve it.

But if you have a friend who is friends with academically-inclined people, you might want to ask them to introduce you.