Take your existing page and turn it into a template in DW. That way the rest of the steps will be applicable.
I would start by uploading all of the sample files to my server and making sure they work before doing any changes. That way if there are problems with your settings they won't be confused with problems in moving the code to a new page.
If you want to do it on on existing page without creating a template:
It won't work on a .html page, so you would want to rename your page to .php.
Then you could copy all of the code before the <html> tag on the sample page and paste it to your existing page.
Then you could copy the <form> and all of its contents from the sample page to your existing page where you want the form to be displayed.
Then copy and paste any <script> tags from the sample page to your existing page.
That should be it. The functionality is achieved through server code, an html form, and client scripts so once you copy and paste those things it should work on any page.