Your style.css file lives in the template folder - wp-content/templates/yourtemplate/
You can also get to it from the WordPress dashboard - Appearance > Editor.
The easiest way to make a Child Theme if you're just going to edit the CSS is to use a plug in like Child Themify: http://wordpress.org/support/plugin/child-themify
To use this particular plugin, install it, then go to Appearance > Themes, where you will see the theme you have activated currently with an option underneath it to make a Child Theme. Click that, then when you see the Child Theme in the list of available themes, activate it. All of the original theme's options and things will still be available to you with the Child Theme activated.
Then you can add any custom CSS you want to the newly created style.css file in the Child Theme folder, all through the Dashboard editor.