How to create a “latest news” page showing a list of posts from blog category

Probably the get_posts tag. It’s simple, you just need a loop.

<?php
   $args = array( 'numberposts' => 5, 'cat' => 5 );
   $postslist = get_posts( $args );
   foreach ($postslist as $post) :  setup_postdata($post); ?> 
   <div>
    <?php the_date(); ?>
    <br />
    <?php the_title(); ?>   
    <?php the_excerpt(); ?>
   </div>
<?php endforeach; ?>

That will show the last 5 posts from the category with ID 5. Complete parameters list.