Here’s a 10 minute video from Texas State Technical College, Harlingen (http://www.harlingen.tstc.edu/) that showcases the use of the assignment module in Moodle. From creating the module, to configuring the various options to grading the assignment once submissions have come in. This video covers the essentials including an overview of each assignment type (offline, upload, etc.).
One note, the narrator mentioned that Moodle’s Rubrics are “terrible”. I’m not in agreement and have used them pretty successfully. There are other great rubric tools out there (and ones that integrate to Moodle) but for a low cost option Moodle’s rubrics can be powerful.
Video link: http://www.youtube.com/watch?v=Uf6yNlBdKvo