The easiest way I know of is to copy your index.php file to a new one called home.php
WordPress will use home.php for the home page of your site if it finds one, otherwise it will use index.php, or a different template that you specify by changing your blog settings (much more complicated).
So just copy index.php to home.php, then add this line right before the Loop starts, using your correct category ID instead of the "xx" I show in this example:
<?php query_posts('cat=xx); ?>
You can also use the category name or slug like this:
`<?php query_posts('category=category-slug-name'); ?>'
You can also use this to limit the number of posts on your homepage to be different from the number of posts shown on other pages as set in your blog Settings>Reading>blog pages show at most number of posts......
<?php query_posts('cat=8&showposts=4'); ?>
Also be sure to read this page from the Codex - it gives good examples and explains how to use the parameters