Could be as simple as adding the_author() template tag to your index.php file.
See:
Template_Tags/the_author
If you need more help you might want to provide a link…
can you link me up? where do I look? I am new to wordpress
I have the POOL theme by the way…
you want me to provide a link to?
Since you’re going to be modifying your theme you might want to take a look at these:
Templates
Template_Tags
Template_Tags/the_author
I didn’t test this but in your wp-content/themes/pool/index.php try replacing:
<small><?php the_time('F j, Y on g:i a'); ?> | In <?php the_category(', ') ?> | <?php comments_popup_link('No Comments', '1 Comment', '% Comments'); ?></small>
with
<small>By <?php the_author(); ?> | <?php the_time('F j, Y on g:i a'); ?> | In <?php the_category(', ') ?> | <?php comments_popup_link('No Comments', '1 Comment', '% Comments'); ?></small>