Widgetizing

I have run a number of wordpress websites for several years, all using the same simple (single file) theme. This was before sidebars/widgets etc.,

I am trying to use a widget which works fine in a new default installation but doesn’t work with my theme (the widget doesn’t show). I have read
http://codex.wordpress.org/Widgetizing_Themes but can’t make much sense of it.

Can any kind sole help in bringing the theme up-to-date?

I don’t use comments so my Main Content area is simply:

<!– S T A R T M A I N C O N T E N T –>
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>

<div class=”post”>
<h3 class=”storytitle” id=”post-<?php the_ID(); ?>”>” rel=”bookmark”>
<?php the_title(); ?>
</h3>
<div class=”storycontent”>
<?php the_content(__(‘(more…)’)); ?>
</div>
</div>
<div align=”center”>
<img src='<?php bloginfo(‘template_directory’); ?>/images/postend.gif’>
</div>
<?php endwhile; else: ?>
<p>
<?php _e(‘Sorry, no posts matched your criteria.’); ?>
</p>
<?php endif; ?>
<h3>
<?php posts_nav_link(‘ — ‘, __(‘« Previous Page’), __(‘Next Page »’)); ?>
</h3>
<!– E N D M A I N C O N T E N T –>