How to theme output from module?
You could use hook_theme to register your theme function, but it sounds like you're wanting output an item list which can be done with theme_item_list:

  $names = array('one','two','three');
  $block['content'] = theme('item_list', array(
    'items' =&gt; $names,
    'title' =&gt; t('My Names'),
  ));


This will fill in your block's content with this:

&lt;div class="item-list"&gt;
  &lt;h3&gt;My Names&lt;/h3&gt;
  &lt;ul&gt;&lt;li class="first"&gt;one&lt;/li&gt;&lt;li&gt;two&lt;/li&gt;&lt;li class="last"&gt;three&lt;/li&gt;&lt;/ul&gt;
&lt;/div&gt;