The best way is using sites like meetup.com and finding an interest group. I met my current friend group (around 20 people) and wife. I ended up joining a group in the beginning and then taking the group over. While we don't use the site anymore and group disbanded, we are all still really close and meet at least a couple of times/month.

Random interactions are going to be hard and awkward. It's much easier to be part of a group that you know the other person has at least some of the same things in common as you.