If you want to change more than just the stylesheet, your child theme can override any file in the parent theme: simply include a file of the same name in the child theme directory, and it will override the equivalent file in the parent theme directory when your site loads. For instance, if you want to change the PHP code for the site header, you can include a header.php in your child theme's directory, and that file will be used instead of the parent theme's header.php.
When you need to include files that reside within your child theme's directory structure, you will use get_stylesheet_directory(). Because the parent template's style.css is replaced by your child theme's style.css, and your style.css resides in the root of your child theme's subdirectory, get_stylesheet_directory() points to your child theme's directory (not the parent theme's directory).
Here's an example, using require_once, that shows how you can use get_stylesheet_directory when referencing a file stored within your child theme's directory structure.