Update: Facebook’s move to enable page tabs based on HTML iframes rather than FBML makes the specific techniques discussed below obsolete. Today I recommend instead using my Facebook Tab Manager for WordPress if your site is on WordPress. If you are not on WordPress, you should find that the task of integrating custom content including contact forms is now easier, overall.
As a sequel to my post on why Facebook Ads Should Point to a Facebook Page (Not an External Web Page), I cooked up a little homegrown tool that generates the required code. The source code output is derived from the example in George Huger’s Submitting a Contact Form via AJAX From Your Facebook Page. Huger shows how to use JavaScript functions that are approved for use within Facebook to submit a data entry form from within Facebook, have it processed on your web server, and get back an acknowledgement you can display on your Facebook page – without ever making the user leave Facebook and go to your website.