You need to find what is called the loop. It startes a little bit like this:
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
and finishes like:
<?php endwhile; endif; ?>
In between these two points, you can include any number of template tags. These tags tell wordress which parts of the post you would like to see, examples include the_title(), the_content(), the_permalink() and the_date(). These will print that data to the loop.
In this instance, you need to find the loop that is displaying your titles (if it as untouched installation, and you are on the front page, probably the index.php from within your theme folder), find the opening line of the loop and slot in the line . This will display all of the content of the post. If this proves too much for that page, you can change it to