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Ikem found a good challenge for getting started with GeoGebra (with a little bit of math to make it interesting).
Draw a line segment AC. Now create a square whose diagonal is AC.
If you are new to GeoGebra - try following this screencast with my construction: http://www.screencast.com/t/fN9F3rEs
Write me if you get stuck anywhere - with the math, with the GeoGebra, with putting it on your page, ....
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(By the way - if you want to try a strict compass and straightedge construction - here is a ggb file with a restricted toolbar: http://mathcasts.org/gg/construct/BasicConstruct.ggb (Info on strict compass and straightedge with ggb here: http://geogebrawiki.wikispaces.com/Compass-and-Straightedge.)
Long version of above link: http://www.screencast.com/users/LFS/folders/Jing/media/4c2edef2-0e2f-47f...
Also, I meant to add that I think you can see the "rules" for diagonals of squares with folding. Take 2 square pieces of paper. Fold one into quarters horizontally/vertically. Fold the 2nd into quarters diagonally. See what you notice about the diagonals. (Aside from the construction, I thought this fold interesting that the different kinds of quarters must have equal area.)
USE either of the links at the END of your emails. For some reason the ones within the letters do NOT work. (Have I mentioned how much I love forums not.)