Do you mean that you want to write a Page that will show only posts from a certain category, like a “Writing” category page? query_posts is what you’d want to use. Give this a shot:
<?php
/*
Template Name: Test
*/
?>
<?php query_posts('category_name=yourcategoryname');
while (have_posts()) : the_post();
// do whatever you want
?>
<a href="<?php the_permalink() ?>" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a>
<?php
endwhile;
?>
Paste that into a PHP file, let’s say test.php, and upload it to your theme folder. Then create a Page (don’t type anything in the page itself) and select Test from the Page Template list. Visit the page and see what happens. Here’s some reading:
http://codex.wordpress.org/Pages#Page_Templates
Is there a reason you can’t just use the specific category page instead of creating a new page? It seems like you’re creating a page to display something that you can already do automatically with WordPress. Let me know how I’m misunderstanding.