To save your work, you simply have to save and export it.
To save your movie, go to 'File> Save as' and save it as what
you want to. To Export your movie, so you can use it on your
web page, go to 'File > Export Movie' and save your movie as
what you want. Normal Flash movies are saved as .swf format.
Publishing your movie can be done in different way. You can
publish an HTML document, have your .swf file and some other
files such as gifs, jpgs, or bmps. To set up your publish
settings, go to 'File> Publish Settings', select the types of
publishing you want, then select OK. To publish the movie, go
to 'File> Publish' or hit F12 on your keyboard. That's it, you
can now use your movie on the web.