The documentation for PostgreSQLDatabase states:
To connect to PostgreSQL, you need to have a PostgreSQL server installed on either your computer or an accessible server.Nice.
Question: how do I do that ?
you install the server software at a free pc or you rent a vps with linux or windows os and install it there.
www.postgresql.org/download
there is also a free database management tool.
Valentina Studio
Thank you Markus and brian.
Emile, if you’re using it to try on a single (mac) computer, use instead postgresapp, a single app you launch it the server is running. you quit the app the server is stopped.
https://postgresapp.com/
For testing (on Mac) I think the postgres app is probably the easies to get started. I had a problem with the download AND the PGAdmin tool with the installer as they were not signed properly. In our installer, we use the binary files and sign them ourselves.
No problem with the PC installer from the postgreSQL website.
Lee
dunno if the PG installers from EnterpriseDB’s site are signed or not
macOS 10.12 only. I will download a Legacy app.
The Legacy application I downloaded is not signed.
Thank you all.
For testing and development purposes you can install a Linux VM (Virtual box or equivalent) and install Postgresql there, and connect your app to it. That’s great to learn the troubles you have to set it up correctly in the cloud or a datacenter. Installing it is just a few terminal commands. But there are few tasks more to enable connections beyond 127.0.0.1. If you use a linux with GUI (desktop version, instead of server version) you can install PGAdmin THERE.
When I read questions from FileMaker users about how to connect to a data base with Xojo, I do not understand the question.
Now I understand.
Where in the Xojo documentation is the PostGreSQL Creation File, Add TABLEs, etc.
We have that for sqlite in the SQLiteDataBase page. In PostgreSQLDatabase there is only an example to how connect to a Data Base (recall something ? FileMaker)
In the mean time, I totally forgot why I put my feet there 
It seems that I was attempting the same as today in last september there (there is an empty Builds folder in my PostgreSQL folder):
PostgreSQL:PostgreSQLExample.xojo_binary_project
That example allows the creation, TABLE addition, Row Addition. Strange.
This is 21st century, not dark ages!
60 or more years ago, to be a registered person @ SACEM (French equivalent of ASCAP / BMI), you have to have been presented (sponsored ?) by someone who is already IN (cooptation ?).
Now I understand what are feeling FileMaker users that ask how to deal with Data Base with Xojo. 
Why Xojo ask me for a license when I want to build the project example ?
I loaded another project, and it does not ask me that.
Are you using a Lite License? DB servers are for Desktop Licenses and beyond… Lite only accepts SQLite.