I have a custom field that is an unordered list that I want to be placed under a static title and to the left of an advertisement. I only want this to show on article pages, but right now I can't seem to figure out how to place the custom field where I want it to be placed. I know a module is required, but what I am asking is if anyone can give me the correct hooks or whatever to retrieve the custom field information, so I can place it where needed.
Copy node.tpl.php of your theme and name it node--article.tpl.php. In this file create the html structure you like. In this file you have access to the individual fields.
<?php print render($content['field_customfieldname']); ?>
will print out content of your custom field. Wrap this filed with html id or class and style it with css. (I am assuming you are working with a non core theme)
I'm a big proponent (and co-maintainer) of the Panels module, which gives you a UI where you can arrange your fields. It takes work to learn how to use it, but it's well worth it in my opinion. :)