I have to remove HTML code that shows up on each page, where is it coming from? I am very inexperienced in Drupal.  I have been asked to remove commented HTML code that appears on each page of the website.  What file should I look for in the root directory to find the source of this? 

The comment was added by another developer as a joke or something.  It's only wrapped in the body and appears close to the top.

The site is using Drupal 6.
It's probably your theme files then, in /sites/all/themes/[selected theme]. You can also try to change the theme and check if it is gone.

Have a look at html.tpl.php and page.tpl.php files.