Dynamic forms - using radio buttons to show form items

I have a form ( a partial) that asks for required data, after the
required form fields, I need to have a radio button that when clicked
shows more fields the user can fill out.

I can not for the life of me figure out how to get the radio button to
show the rest of the form. I have tried:
form_remote_tag and AJAX (tried to recreate the Agile book example)

Any help is appreciated but code examples are most helpful.

Thanks in advance. -K