I would assume that I should be backing up the SQL database files that PC Monitor is using. Would I run the backup through the SQL Server Management Studio? The PC Monitor software doesn't have a means to run an SQL backup....correct? Just run the normal SQL backups? 

You can setup with SSMS a backup job that is set to only run manually. Then if you have SQL Server Agent server set to start automatically you can control the backup job from PC Monitor and you can see the output too.