I used to set up environment evariables http_proxy and https_proxy (with user + password) in the past to use Pip (on Windows) behind a corporate proxy. But recently I needed to tell Pip to use a proxy without setting up environment variables as this conflicted with git configuration in combination with SSL Certificates which I get to work only by removing environment variables for proxy.
Fortunately you can configure PIP with an pip.ini file as described here: https://pip.pypa.io/en/stable/user_guide/#config-file
The detailed answer to my own question follows below.
Here are the steps how to configure proxy (with auth.) in pip's config file (pip.ini)
edit pip.ini file and add
[global]
proxy = http://user:password@proxy_name:port
Example for proxy with authentification (user + password):
proxy = http://butch:secret@proxyname:1234
proxyname can be an IP adress, too
Example for proxy without auth.:
proxy = http://proxyname:1234