I was wondering how I would go about upgrading my forum software from 2.0.19-2.0.22. I have never updated before and since I'm a few versions behind I don't know which to download or what to do exactly.
That depends. Have you installed any MODifications? The update method differs if you have.
For MODded boards you will need to download the Code Changes packages and upgrade in steps .19>.20>.21>.22
If you have not installed MODs then download the Changed Files Only package. Upload the files from the .19>.22 package and then the install directory. Point your browser to yoursite/yourforum/install/update_to_latest.php. Once complete delete the install directory.