mosListMessenger has a page in the mosLM Control Panel called "End User Tools. This page gives clear code examples that can be copied and pasted into Joomla Modules in order to allow you to display the Newsletter Subscription form on your website.

To create a new module (FIRST: DISABLE ANY WYSIWYG EDITORS!!!) simply copy the HTML from the examples on the "End User Tools" page and then go to the Module Manager in Joomla Admin, then click New, paste in the html code into the textarea at the bottom, add a title and select which pages to show on and then click save.  This will create the new module for you.