I'll give you one word of warning, and that is that making flash forms can be stunningly simple, or overly complex. Sadly it is usually the latter. As marsian said, you need to have a PHP or ASP backend, and you can find some good tutorials on accessing either in flash from the flashkit tutorials.
My suggestion is taking it slow and try making a form with only one field to submit until you get it to work, then expand. Makes figuring out errors much easier.