Website not accessible? How to resolve "Server not found" issues when attempting to browse sites?

While attempting to browse some sites, we sometimes encounter the error "Server not found". For example, while attempting to browse YouTube, a Firefox browser might through the error -

Server not found
Firefox can't find the server at www.youtube.com ....

as shown in the image above.

How to resolve "Server not found" issues when attempting to browse sites?

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