Joomla! Documentation™

You need two files: /modules/mod_latesnews/helper.php and /modules/mod_latesnews/tmpl/default.php

In the helper.php, add the

$lists[$i]->creationdate = JHTML::_('date', $row->created, JText::_('DATE_FORMAT_LC4'));

line to the bottom, so:

foreach ( $rows as $row )
{
  $lists[$i]->link = JRoute::_(ContentHelperRoute::getArticleRoute($row->slug, $row->catslug, $row->sectionid));
  $lists[$i]->text = htmlspecialchars( $row->title );
  $lists[$i]->creationdate = JHTML::_('date', $row->created, JText::_('DATE_FORMAT_LC4'));
  $i++;
}

Now when the dates are collected with the mysql query, you need to add them to the default.php. Change this code

<a href="<?php echo $item->link; ?>" class="latestnews<?php echo $params->get('moduleclass_sfx'); ?>">
  <?php echo $item->text; ?></a>

to

<a href="<?php echo $item->link; ?>" class="latestnews<?php echo $params->get('moduleclass_sfx'); ?>">
  <?php echo $item->text .'<br />'.$item->creationdate; ?></a>

If you only want on line, like this
07.06.10 My new news
you need this code:

  <?php echo $item->creationdate .'&nbsp;&nbsp;&nbsp;' ?>
  <a href="<?php echo $item->link; ?>" class="latestnews<?php echo $params->get('moduleclass_sfx'); ?>">
      <?php echo $item->text; ?></a>