Your “blog” page will need to have a custom wordpress loop which queries posts belonging to the “blog” category.
For example:
<ul>
<?php
$blog_query = new WP_Query("cat=18&showposts=3");
$wp_query->in_the_loop = true;
while ($blog_query->have_posts()) : $blog_query->the_post(); ?>
<li>
<span class="date">Posted: <?php the_time('F jS, Y') ?></span>
<h3><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h3>
<p><?php the_excerpt(); ?></p>
</li>
<?php endwhile; ?>
</ul>
In the above example pay special attention to cat=18&showposts=3
the 18 should be replaced by the category id number of your blog category and you can remove or change the 3 to how many posts you want to show.
Hope that helps.
Aaron