In the FAQ http://www.zenphoto.org/2008/08/installation-and-upgrading/ it tells me to change files. Do I do that on the server side or on my own machine?

Then in the upload of the new version, a zip file - where do I unzip it? first on my own side and the ftp a whole new installation?

Why do you double post? Didn't you read the red note?

Unzip of course before uploading. Then upload the new files to your server where you want to upgrade the installation.