Cam Studio is an open source screencasting application for Windows. You can find the application at http://camstudio.org/.
There should be no issue for instructional use on a teacher computer. You may have to ask your tech guy to install it, but since its open source it should not be a big deal.
So in the following screencast I use Cam Studio to show you how to download, install, an use Cam Studio. Let the screen-casting begin.
Let me know how it all goes.