You don't have to be an administrator to install GeoGebra but you need Java. You can download Java here. You must be an administrator in order to install Java. Most schools have Java installed on the computers; if not, tell your system administrator to install it!

You can download GeoGebra from http://www.geogebra.org/cms/. Click on Download. You have two download options:

WebStart: You don't have to be an administrator to do this installation, GeoGebra isn't installed into the computer registry. If you are online the program will be upgraded every time there is a new release. After the installation you can still use the program even when you are offline.
Applet Start: GeoGebra appear on a new webpage, you can run it on the Internet.

On the GeoGebra-homepage you can find an excellent user forum, and a Wiki.