One of the best places to use the non-verbal ‘invitation’ to meet people is at a coffee shop. 
Go to your local coffee shop and take something, such as a backpack or a briefcase with you. Sit at an empty table which is adjacent to another empty table and place your backpack on the table next to yours. The backpack will keep other people away from the table next to you. As long as there are other free tables, most people won’t bother you.
If you see someone interesting come in the door, make brief eye contact. Not too long to be annoying, but long enough to say that you are interested. Then when they are looking for a table, remove your backpack from the empty table. This is your non-verbal invitation. If the person is interested in you, chances are VERY good that they will accept your non-verbal invitation and sit next to you. Then all you have to do is start up the conversation with an innocent comment, such as “That coffee looks great. What is it?” If they are interested, you will notice it in their response and/or smile. Then all you have to do is keep the conversation going as discussed in the section on How To Meet People.
This same non-verbal invitation will work in many scenarios. If you are on a bus or train, hold your newspaper open so that it blocks the free seat next to you. If someone is walking by that interests you, make eye-contact briefly, then close your newspaper to free the seat next to you. There is a very good chance that they will accept your non-verbal invitation and join you.
Why does the non-verbal invitation work? When you remove your backpack, it will appear that you are being polite and offering a space. Most people respond to courtesy with courtesy. Unless you are frightening to look at, or they suspect that you have intentions that do not interest them, they will very likely accept your politeness and sit in the table you have provided. Try it. It will not work every time, but more often than you can imagine.