Edit the config.inc.php file found in the admin folder. You need to fill out the details of your MySQL server. Then simply upload the entire guestbook folder and run the install script by visiting it in your browser. Once installed delete the install.php file.
I'm assuming you are using Advanced Guestbook 2.2. A search of these forums using the search feature would provide you with multiple threads on the matter of this guestbooks vulnerability and the fix for it.
Hmmm the method of uploading may be causing the problem. I remember back when I was playing with Invisions file manager I made some files using it but could not edit, nor delete, these files via my FTP client. So you could be right about access rights being the problem.
Does the schools server run on windows and your hosts server run on nix? There are major differences between the way windows handles somethings and the way nix does.