How do I attach my registration page to a new web site without recreating the page?

Do you mean to ask if how you can embed the same form to another website? If yes, just simply grab the embed codes again and paste it to the web editor. We recommend our iframe method: http://www.jotform.com/help/148-Getting-the-Form-iFrame-Code.

If you want to track down if what website the form is filled and submitted, you can add the Get Referrer widget to your form:

http://widgets.jotform.com/widget/get_referrer

Here's our guide to add a widget in a form: http://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form. 

Thanks