Assuming you are asking how to NOT show the date of posts where you display the posts to visitors, then if you are using the WordPress Default 1.6 theme, you would delete the template tag, the_time(), in the wp-content/themes/default/index.php script file.
Probably would delete this whole line:
<small><?php the_time('F jS, Y') ?> <!-- by <?php the_author() ?> --></small>