Without knowing your theme or seeing your site, I can only suggest you will need to move the template tag, the_time or the_date, in your theme’s index.php file.
See:
Stepping into Template Tags
Stepping into Templates
Template Hierarchy
Editing Files
Look in your theme’s index.php and locate the_title and the_time (or the_date).
You want to move all the code pertaining to the_time or the_date to after the_title.
For example, in the following code:
<div><h2 id="post-<?php the_ID(); ?>"><a href="<?php the_permalink() ?>" rel="bookmark" title="Permanent Link to <?php the_title(); ?>"><?php the_title(); ?></a></h2><?php the_time('F js, Y') ?></div>
I moved <?php the_time('F js, Y') ?> to after everything between the <h2> and </h2> tags (which contain the_title).
