CSS is something very different. However, if you need to insert some php code or make any changes to the actual theme file(s), it’s highly recommended you use the child theme method. This will allow you to keep your theme updated without losing your custom code and/or changes.
I’m not sure what code you are inserting or what their instructions are, but you would be adding it to the header.php file of your theme. Although, you will definitely need to be careful where this goes because there will obviously be other elements that have to provide room for your “like” box.
Before you do anything though, I would recommend you make a backup of your theme first, just in case you need to reverse what you do or make a mistake…even when using a child theme.
As a side note, I just noticed you are using the Resonar theme from wordpress.com which is for the “hosted” version of WordPress. So your posting here might have to go to their support because themes from .com are only for the hosted version of WordPress.
The other thing too is that I believe that users of their themes are limited to what they can customize themselves. However, for the standalone WordPress (here at www.remarpro.com), that is a different story.