I can only give you an idea of how I would do it.
You can use jQuery and bind a click event to the forms button. When the button is clicked a callback function will show the iframe, which was previously hidden by jQuery. If you want the iframe to show in a popup, there are many examples of using jQuery to show contents of a DIV element in a popup.
If your starting out, using something like NetBeans php as your editor will help, it has Code Complete as a feature. You'll need to add the jQuery library to your project. I'm assuming your developing locally using a LAMP (Linux, Apache, MySQL, PHP) or WAMP (same as LAMP but running on windows not linux). I say it will help be because it will expose methods of the library, however the jQuery API documentation is really good.
Good Luck !