If the person you want to protect the files from is logging in to the computer with a different user name, then it's easy -- just set the file permissions so that only the file owner can read it.
(setting file permissions -- command line: use the chmod command; in KDE: right-click on the file, and select 'permissions')
If the other person is logging in to the machine using the same login credentials as you, then you're missing all the fun: Linux is a fully multi-user system; each person can have their own log in, and once they're logged in, its like they've got the system to themselves -- they can then set up the environment just how they like it without interfering with anyone else's settings.
I guess it's just possible that you have two people using the same login, and you really don't want to have to change that (maybe you both share the same mailbox or something?). In that case, you're going to need to encrypt the files or something like that. You could log in as root and change the permissions to that only the root user can see the files, but that's not really what you should be using the root login for.
Hope that helps.