I have a website, and the editing file in front of me, but I don't know how to get the HTML from THIS page to mine!
Hey there. You may edit the HTML code of your page with many software products (even with the Windows default Notepad). Dreamweaver is the most comfortable I think so you should use it. After you do all the necessary changes to the page just upload it to your host again (replace the old file or just replace the section of the code). Besides, you might want to know some basics of HTML editing. Read couple of short HTML tutorials, they are all available free on the Internet. Just search for "html tutorials".
With a FTP program such as SmartFTP or Filezilla or any of the many other ones out their will allow you to upload your files to your web. And as el tenedor said use your editor copy the html you need to your page, make your changes and then upload to your site.
you dont even need a program ftp you could use windows ftp aswell by putting ftp://yourwebsite.com and that should work