You have 2 different kind of proxies here, a public and a private proxy. Private proxies are typically a paid service where you create an account and then pay for the services that company offers. Whereas public proxies are available to everyone. There are pros and cons to each, but that is for a different discussion.
In the example of the site you linked, they're typing their username and password, of their private proxy account, and then the proxy sites URL.
Maybe a better example would be to go try NordVPN. They offer a VPN solution but also offer a proxy service that acts this exact way when connecting to their proxy servers. I use NordVPN mostly as a VPN, but have successfully used the proxy as well. You should also keep in mind that if you setup authentication for a proxy on a web browser, you typically are given a GUI to setup this information. The example you linked and what I wrote, are usually ran from the command line.