different catergory post styles

Ive looked for an answer for this on the board, and though I found some answers – they were either really poorly answered, too complicated for me to understand or utilised some plugin that some guy made that didn’t have any instructions, so please bear with me

As far as I understand wordpress (not alot) it uses the index.php to form the structure of the posts on the front page of your blog. Say for example in my stylesheet I made the post background blue – so all the posts on the front page of the blog have blue background. But say I wanted a all posts that are in a specific catergory to have a different back ground. So i put the css code in the style sheet for the these posts to have a green background.

How do I make those posts in this catergory get the css for the different background considering all wordpress post use the index.php?? Is there some way to get wordpress to pull a different template/index2.php for these special catergory posts??

any help would be greatly appreciated