Microsoft Movie Maker is a pretty easy and basic program to use for editing video. 

The Pros for using it:  It's a Free download so you can easily get it at home too, it's relatively easy to use and there are lots of online tutorials to help you out, you can use video from a camera or existing video, and it's great for a short internet video.

The Cons to using it:  You might have problems turning your video into a DVD that will work on any DVD player.   Here's some more information about Burning a Movie Maker Video to a DVD.

For help using Windows Movie Maker try this outstanding tutorial from Saskatchewan Schools in Canada:  http://www.saskschools.ca/resources/techref/moviemaker/movie.html

The newest version of Movie Maker for Windows 7 is available online:
http://explore.live.com/windows-live-movie-maker?os=other
 

Free Online Video Editors
Also available to anyone with internet access are some free online video editors.  You might have to register with them but without even downloading anything you can start editing video online for free.  Here is a review of four online video editors.

YouTube Video Editor                 Creaza                 Pixorial

Making Your Own Video Tutorials
Wouldn't it be great if you could just show your students how to do something on the computer?  Here's a quick tutorial about using the screen recorder that came with the SMARTBoard Notebook software:

SMART Notebook 10.0 - Recorder
By Marcia Jeans, Instructional Technology Specialist at USD259 in Kansas