Displaying posts by category in separate sections

I need to build a blog that has three separate sections on the “home” page. For instance, a jazz, a folk and a rock section. Posts would be given a specific category. Then the posts would display on the page in the section for which they have been coded. I’m assuming this is possible, that it would simply require writing the PHP code on the home page to look for the category information in a post and then pull it into the proper section. Just wondering if anyone has any experience with this or could point me in the right direction, maybe a tutorial or an example or something. Thanks for any help!