How do I create and connect a WordPress child theme?

I'm in the process of designing a website and would like to customize it through a child theme to avoid modifying the parent theme directly and to ensure that future updates don't lose custom content. However, I'm not sure how to begin creating a child theme, and it's not clear how to effectively add custom features and styles to a child theme.

How do I create and connect a WordPress child theme? What are the advantages of a child theme and how do I add custom features and styles to it?