Child Themes – basics question

I love using child themes to customize sites, and so far I’ve mostly had to just make CSS changes. So I make a child theme and create a new style.css page.

My question is about more complex theme customization. Say I want to modify a php page in a parent theme – functions.php or something like that. I want to make sure I’m understanding the process to do it correctly. In this example, I would:
-1- put a file in my child theme folder called functions.php
-2- include only the php code I want to change (correct?)
-3- do I need some sort of include statement in this file to include the contents of the original file? (like the “@import url()” line in the css file)

Am I getting it right? Anything else I should know?? TIA!