Saving a document in Stykz is just like saving documents in other applications (File > Save...):
Pivot Compatibility Note
If you are just starting to use Stykz after having worked with Pivot for a while, you may try to use File > Save to export an animated GIF image from Stykz (since this is the way Pivot did it). However the File > Save and File > Save as... menu options are only for saving Stykz document files. If you want to export your animation to GIF (or QuickTime .mov, or a sequence of images), you will need to select File > Export Animation... instead. For more information (including the reason Stykz does things this way), see the Saving vs. Exporting topic.