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In your template.php file, after you've set your standard arguments you can add some based on categories it picks out of the url

if (!empty($_GET['category'])) {
    $queryCategory = $_GET['category'];
    $args['category_name'] = $queryCategory;
}

Then just make sure to have links on your page that go to currentpage?category=some_slug

Then the filter will be added to your query arguments and the posts on the page will get filtered!

Note that the word category can be changed to anything; I was just using categories on my example :)