You have several options - depending on how closely you want the new sign-up form to reflect the existing form...and how much effort you are willing to apply.
If you do not want to write any code,
You can do *almost* exactly the same thing by using the SiteVisitorSignUp box. See the FAQ here:
That interactive process will create html for you, which you can insert into your home page.
That Site Visitor SignUp Box form does not have an 'unsubscribe' option (however, in looking at the current form on your website, unsubscribe was an awkward process with that dialog).
The contact can of course unsubscribe from the footer of any email you send them.
If you want the functionality to be exactly the same as your form, you will need to write some php to implement that behavior. I expect that the script you would need to write is much like the script you reference in your form (box.php), so you could start with that script. See the "Creating a Contact" and "Opting-out a Contact" sections of the Contacts Collection for detail on how to create or Opt-out a contact via the API.
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