Yes, you would create the child theme and copy the changed files to the child theme -- but you will need to carefully read about how functions.php work in a child theme -- it's not the same as regular php files. With the css file, it's better to only have your changes in the child theme style.css file, so you may need to use a compare text editor or other program to do those. Or, less ideal, you can copy the entire thing -- though that will make it harder to keep track of and manage your CSS and it creates duplicate code.
Also, when you change to a child theme, theme options don't carry over, so you'll have to redo those in the child theme.
Once you have everything set in the child theme, you can the update the parent theme.
All that said, be very, very sure to make multiple archive (backup versions) of your files as you are working. And a complete backup of everything before you start messing with it.