Once you have your child theme, add the new rules to the end of your style sheet.
If I were you, I'd create a minimal child theme that acts exactly like the parent theme (i.e. a child theme with just a style.css file with the mandatory comments---theme name, and template directory---and an @import statement to reference the parent style sheet). When you activate this, you'll possibly have to redo some of your Dashboard settings, but apart from that it should look exactly like a vanilla install of your theme.
You can then add your style modifications to the end of your minimal style sheet. In particular, if you've already made changes to your parent theme style sheet, you need to transfer those changes to your child theme style sheet, after which you should replace the parent theme's style sheet with a vanilla version (after saving the altered one, of course, in case you need it later---if you forgot to transfer an alteration, for example).