You pretty much always need a server in order to send email. There are lots of tutorials available online for how to do this on the server side, and many web hosts will actually set you up with a bunch of free scripts that can do this for you.
Talking to a server is a bit out of the scope of Flash Catalyst 1.0. But if you import your Catalyst project into Flash Builder, you should be able to get there by writing just a little bit of code. You'll want to use HTTPService to post the data (email address, etc.) to your server script, which in turn will send the email. There are tons of tutorials online about using HTTPService, but if you get stuck on this part feel free to post a question at http://forums.adobe.com/community/labs/gumbo/
Hope that helps!