How do I get more dwellers to automatically come to my Vault?
When you have 20 dwellers living in your vault, you can build a radio station. This will attract people from the outlands to you.
Another way is to complete objectives by getting enough caps to earn lunch boxes — or you can buy them — which sometimes contain cards that award a new dweller with nice skills and equipment.
radio station not working for me ... I'm baby making all the way just make sure your not trying to mate family as this don't work .... just try upgrading a 3 wide living quarters and filling it with both sex they will pair up and start the process :)