Step 1: Note the default printer and default browser for the existing profile (or any other things that may be unique to the profile, but those are the two big ones). You might note which programs have been logged in with credentials you don't have as well - Dropbox, Google Drive, Skype, etc
Step 2: Log in with an account that has local administrator privileges.
Step 3: Edit the registry and go to HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows NT\CurrentVersion\ProfileList
Look at the various keys in there and find the one with the value that you want to delete. For example, in the screen shot below, the value c:\users\dave is in the key that begins with S-1-15-21. You delete the entire entry that begins with S-1-15-21.
Step 4: Rename the profile that is going to be deleted. In this example, I'd rename c:\users\dave to c:\users\dave-old
Step 5: Reboot and then log in as the user. You'll find a brand new profile is created and you can access all the old data in the renamed profile from step 4.
Step 6: Set up the profile as needed including, but not limited to:
1) set up Outlook
2) move back data from old profile to new profile:
c) all the other stuff that is in c:\users\%username%
3) set up backup
4) set up VPN
5) add back signature using old sent items
6) add printers (if necessary) and set correct default printer
7) restore browser settings
8) Remind the user that he/she will need to log in to services you don't have the password to (Dropbox, Skype, Google Drive, etc)