When we are retired and our nests are empty, new friendships are almost up to the fates, because as we get older, we somehow forget or lose our ability to make new friends. Things are even harder for those who live remotely or don't get out frequently.
Adults meet others when walking the dog, joining a class (art, dance, writing etc.), playing a sport, game etc. Some people meet other people through an existing friend. Two things are important: To get out more so you meet more people and secondly, knowing how to make real friends
We all know that a child can make a new friend in less than a minute. When we moved to a new house years ago, our then five year old son knocked on our neighbor's door, pulled a few 'dog eared' cards out of his pocket, and asked point blank if they had a boy about his age so he could show him his card collection. The did have a six year old son and thanks to my cheeky boy, she and I soon became fast friends too, as did our husbands.
Meeting people is the easy part but it's only half the battle. Adults can't use the same approaches that children do and that is unfortunate. If I knocked on your door and asked if you wanted to come out and play, you would probably look at me as if I had two heads and it wouldn't go so well!
As I said, the older you get the harder it is. We can however, learn to express your genuine interest in others, to channel unencumbered candor in positive ways, (the way children do), and to give of ourselves more and not expect anything in return, the same way children do. When someone genuinely enjoys your company and visa versa and you have things in common or interests that you enjoy sharing, that is the foundation of a lasting friendship.