You’ll have to start by creating a form that’s fully functional outside of Facebook, and hosted on your own server.
Then when you have that, create a PAGE on Facebook.
Next step is to create an APP at http://developers.facebook.com, which basically just points to your form.
And finally, you’ll have to add that app to your page, so visitors of the page will see an iframe with your form in it.
Those are the basics of doing it all yourself, pretty much.
Or you could go to a service that does all this for you and has frameworks ready for that. No experience with outsourcing things that way, but there are probably plenty.