Just to add something I was missing from all the answers - even if it seems to be silly and obvious as soon as you know:
The file has to be named "App.config" or "app.config" and can be located in your project at the same level as e.g. Program.cs.
I do not know if other locations are possible, other names (like application.conf, as suggested in the ODP.net documentation) did not work for me.
PS. I started with Visual Studio Code and created a new project with "dotnet new". No configuration file is created in this case, I am sure there are other cases. PPS. You may need to add a nuget package to be able to read the config file, in case of .NET CORE it would be "dotnet add package System.Configuration.ConfigurationManager --version 4.5.0"