The affiliates cannot be registered from the website front end, they can contact the admin through contact us form for further procedure. However if in case you want to create a form where they can enter their details and register then you need to create a custom form and navigate it on the website.
To create the custom form please refer:
Once the form is embedded in static page then you can navigate it by below mentioned steps:
You can add pages to the site from Admin panel-> Site-> Static Pages, edit the content in the static page if required or add a new static page-> Copy Alias of page
To add navigation go to Site-> Navigation-> Edit the relevant section, in the Title mention "Page Name" and in URL mention "/page/alias of page"
Once the key for the affiliate is generated, you can share them with the affiliates via mail.