Outlook can be backed up by copying the .pst file it uses to store information. Search for *.pst looking in hidden files and folders, copy and paste to a different directory. The path should be: root drive (c:), documents and settings, account username, local settings, application data, microsoft, outlook. Unfortunately this method does not backup your email account settings (servers, logon information and passwords). I recommend recording these manually.
Outlook express is a different animal, it uses .dbx files for each folder. You can also backup the emails/ folders by dearching for *.dbx looking in hidden files and folders, copy the files to a different directory. The path should be: root drive (c:), documents and settings, account username, local settings, application data, identities, some numbers between brackets (ex: {6719004D-E77A-4068-A605-15E19D4914C7}), outlook express. Account information can be exported from outlook express using the import export feature.
I do not know of any easy, one step solution to backing up email other than making an image of your hard drive.
Depending on back up method, he could creat a .bat file to xcopy the .pst file to another location.