trying to add author to post

Can you confirm that you placed the_author() inside your loop?

<?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
<!-- some other xhtml template code could go here-->

<p>This post was written by <?php the_author(); ?></p>

<!-- some other xhtml template code could go here-->
<?php endwhile; endif; ?>

Can you post the code that you’re trying to change?

I understand the concept of the loop, but don't know which files affect it.

–Each template page can have its own (or many different) loop(s)…which makes WP really flexible, but also tricky sometimes to determine which file changes what page…

Can you list the php files in your theme?

For example:
index.php
archive.php
single.php

Also, on which page(s) are you trying to add the author name? All pages, just the home page, category page? (it’d probably also help if you could post a link to your site).

I'd like to have the author accompany all posts on all pages.

You’ll need to change each of these files:
index.php
archive.php
page.php
single.php

In index.php change:

<small><?php the_time('F jS, Y') ?> </small>

to

<small><?php the_time('F jS, Y') ?>  by <?php the_author() ?></small>

In archive.php change:

<small><?php the_time('l, F jS, Y') ?></small>

to

<small><?php the_time('l, F jS, Y') ?>  by <?php the_author() ?></small>

In page.php and single.php change:

<h2><?php the_title(); ?></h2>

to

<h2><?php the_title(); ?></h2>
<small>by <?php the_author() ?></small>

Note that you can put any xhtml markup around <?php the_author(); ?> (not just <small> </small>)