At its most-basic, you tell Hazel to monitor a specific directory and give it some rules to execute in the form of standard condition statements “if this then that.” For example, you can have Hazel monitor your Downloads folder for music files and when one hits the folder, Hazel can import it into iTunes and then move the downloaded file to the Trash.
I also have a file-naming convention I use for all files, so I have Hazel doing most of that work (some of the naming requires my input to determine the purpose of the file).
I also have a coffee roasting application that generates auto-save files that need manually deleted so I manage that folder with Hazel as well.
The rule-building process in Hazel is very intuitive with a lot of options/conditions available. I’m still getting used to it and slowly implementing rules but so far I’m really digging it. They provide a free trial as well.
This is quickly becoming one of my “must have apps.”