Table Structure:

Table
article
articlecategory
author
category

The category table lists the main categories while the articlecategory table is a join that lists the

category id and the article id.

On my main page I have all articles listed. However, I would like other pages to contain only stories

from category x, y etc.

I run the query:

$query = 'SELECT * FROM articlecategory WHERE categoryid=3';

but it returns nothing.

You're not running a query there. You would need to use the following:

<?php
//...

$query = mysql_query("SELECT * FROM `articlecategory` WHERE `categoryid` = 3") or die(mysql_error());

if (mysql_num_rows($query) === 0) {
	// You have no categories here. Add some error code.
} else {
	while ($article = mysql_fetch_assoc($query)) {
		// This will loop for each article
		echo "{$article['name']}<br />";
	}
}

//...
?>