Sending environment values like DOCUMENT_ROOT is often blocked at the server end for security reasons, or simply the server is not configured to send that value.
Do not be confusing a URL (
http://www.mydomain.com/whatever) with a filesystem path! They are two different things! One begins where your web server puts its HTML files (like index.php) and the other is where the server stores its files.
The sure way to find out is to go to the phpinfo() link in Reports -> System Information. Scroll to the bottom, where all the SERVER values are listed, and look for _SERVER["SCRIPT_FILENAME"]. On my local environment, it says
/Applications/MAMP/htdocs/0962/manager/index.php
so for my paths I need
/Applications/MAMP/htdocs/0962/assets/
A common Linux hosting path will look like
/home/domain-or-username/public_html
so the path needed would be
/home/domain-or-username/public_html/assets/
The <base> tags mentioned is a meta tag that goes in your template’s head:
<base href="[(base_url)]"></base>
The style of using a closing tag is to make IE play nice with it.