Editor’s note from the future: Quickmail may work for you, but as of 2017 the plugin has been discontinued and it is confirmed to be compatible with Moodle 3.5 or earlier only.
Here’s a quick video (3 minutes) that shows the use of Quickmail in Moodle. Quickmail is a popular 3rd party addon that provides email like functionality within Moodle (an alternative to the somewhat confusing default core messaging system). The video was created by Bergen Community College and is hosted on their channel.
Direct video link: http://www.youtube.com/watch?v=MJBWf_lCFLU