Using Child Themes with Premium Theme

I have been working with WordPress for about three weeks. I absolutely love it. After hacking my premium DynamiX theme to pieces to get what I wanted for appearance, I realized you can use child themes to customize and leave the core code alone. The problem I am having is how to get the changes I want with the child theme. When I add css to the child it does nothing. I am not quite sure which rules or css are responsible for what I would like to change. What I am trying to accomplish is to have a custom background behind an accordian on my home page. The only thing I have been able to achieve is changing the entire page background. This in turn changes all the pages and looks horrible. If anyone has an idea of how to go about this and could lead me in the right direction it would be highly appreciated. At this point I am at a stand still. Thanks in advance for all replies regarding this matter. inclouddesign